# Recent questions tagged infinite

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How many terms of the arithmetic series $3+7+11+\cdots$ will add up to 210 ?
How many terms of the arithmetic series $3+7+11+\cdots$ will add up to 210 ?How many terms of the arithmetic series $3+7+11+\cdots$ will add up to 210 ? ...
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Determine the value of the series: $\sum_{k=4}^{7} 2 k$
Determine the value of the series: $\sum_{k=4}^{7} 2 k$Determine the value of the series: \ \sum_{k=4}^{7} 2 k \ ...
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Determine the value of the series: $\sum_{n=1}^{5}(3 n+2)$
Determine the value of the series: $\sum_{n=1}^{5}(3 n+2)$Determine the value of the series: \ \sum_{n=1}^{5}(3 n+2) \ ...
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Consider the arithmetic series $-4-1+2+\cdots$ Calculate the smallest value of $n$ for which $S_{n}>300$
Consider the arithmetic series $-4-1+2+\cdots$ Calculate the smallest value of $n$ for which $S_{n}>300$Consider the arithmetic series $-4-1+2+\cdots$ Calculate the smallest value of $n$ for which $S_{n}&gt;300$ ...
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Consider the arithmetic series $(-1)+\left(\frac{-3}{2}\right)+(-2)+\cdots+(-16)$.
Consider the arithmetic series $(-1)+\left(\frac{-3}{2}\right)+(-2)+\cdots+(-16)$.Consider the arithmetic series $(-1)+\left(\frac{-3}{2}\right)+(-2)+\cdots+(-16)$ &nbsp; a) Determine the number of terms in this series. b) Calcu ...
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What are the applications of integrals?
What are the applications of integrals?What are the applications of integrals? ...
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What are infinite integrals?
What are infinite integrals?What are infinite integrals? ...
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What is an infinite determinant?
What is an infinite determinant?What is an infinite determinant? ...
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Let $\mathcal{S}$ be the linear space of infinite sequences of real numbers $x:=\left(x_{1}, x_{2}, \ldots\right) .$ Define the linear map $L: \mathcal{S} \rightarrow \mathcal{S}$ byLet $\mathcal{S}$ be the linear space of infinite sequences of real numbers $x:=\left(x_{1}, x_{2}, \ldots\right) .$ Define the linear map $L: \m ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following statements is NOT TRUE? 0 answers 59 views Which of the following statements is NOT TRUE?Which of the following statements is NOT TRUE? &nbsp; (A) \int_{0}^{3} \frac{1}{(x-4)^{2}} d x=\frac{3}{4}. (B) \int_{0}^{3} \frac{1}{(x-4)^{2}} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Consider the series \sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n}. Which of the following statements is TRUE? 0 answers 57 views Consider the series \sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n}. Which of the following statements is TRUE?Consider the series \sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n}. Which of the following statements is TRUE? &nbsp; (A) The series is not conditiona ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let g(x, y)=x^{2} y+\cos y+y \sin x, Which of the following statements is TRUE? 0 answers 41 views Let g(x, y)=x^{2} y+\cos y+y \sin x, Which of the following statements is TRUE?Let g(x, y)=x^{2} y+\cos y+y \sin x Which of the following statements is TRUE? &nbsp; (A) g_{x}=2 x y+\cos y+y \cos x. (B) g_{y}=2 x-\sin y+\s ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Consider the telescoping series \sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right). 0 answers 52 views Consider the telescoping series \sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right).Consider the telescoping series \sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right). ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that the series \sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right) converges and find its sum. 0 answers 64 views Show that the series \sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right) converges and find its sum.Show that the series \sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right) converges and find its sum. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine whether the following series converge or diverge. \sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}} 0 answers 44 views Determine whether the following series converge or diverge. \sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}Determine whether the following series converge or diverge. \sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine whether the following series converge or diverge. \sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n} 0 answers 56 views Determine whether the following series converge or diverge. \sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n}Determine whether the following series converge or diverge. \sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given that \dfrac{1}{1-x}=1+x+x^{2}+x^{3}+\cdots=\sum_{n=0}^{\infty} x^{n}. Write down the power series of \dfrac{1}{1+x^{2}} 0 answers 63 views Given that \dfrac{1}{1-x}=1+x+x^{2}+x^{3}+\cdots=\sum_{n=0}^{\infty} x^{n}. Write down the power series of \dfrac{1}{1+x^{2}}Given that \dfrac{1}{1-x}=1+x+x^{2}+x^{3}+\cdots=\sum_{n=0}^{\infty} x^{n}. Write down the power series of \dfrac{1}{1+x^{2}} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The interval of convergence of the series \sum_{n=1}^{\infty} \dfrac{(-1)^{n}(x+2)^{n}}{n} is 0 answers 49 views The interval of convergence of the series \sum_{n=1}^{\infty} \dfrac{(-1)^{n}(x+2)^{n}}{n} isThe interval of convergence of the series \sum_{n=1}^{\infty} \dfrac{(-1)^{n}(x+2)^{n}}{n} is &nbsp; A. \quad(-3,-1 &nbsp; B. -3,-1 &nbs ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which FIVE of the following statements are TRUE? 0 answers 44 views Which FIVE of the following statements are TRUE?Which FIVE of the following statements are TRUE? &nbsp; A. The series \sum_{n=1}^{\infty}\left(\frac{4 n-3}{3 n-4}\right)^{n} converges &nbsp; B ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If the power series of f at a is given by  f(x)=\sum_{n=0}^{\infty} c_{n}(x-a)^{n}  for |x-a|<R, then 0 answers 47 views If the power series of f at a is given by  f(x)=\sum_{n=0}^{\infty} c_{n}(x-a)^{n}  for |x-a|<R, thenIf the power series of f at a is given by  f(x)=\sum_{n=0}^{\infty} c_{n}(x-a)^{n}  for |x-a|&lt;R, then ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine whether the series \sum_{n \geq 1} \dfrac{1}{\sqrt{n^{3}}} converges or diverges. Give a reason for your answer. 0 answers 50 views Determine whether the series \sum_{n \geq 1} \dfrac{1}{\sqrt{n^{3}}} converges or diverges. Give a reason for your answer. Determine whether the series \sum_{n \geq 1} \dfrac{1}{\sqrt{n^{3}}} converges or diverges. Give a reason for your answer. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the sum of the series \sum_{n \geq 2} \frac{2}{n^{2}-1} 0 answers 67 views Find the sum of the series \sum_{n \geq 2} \frac{2}{n^{2}-1}Find the sum of the series \sum_{n \geq 2} \frac{2}{n^{2}-1} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0 0 answers 41 views Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Which of the following statements is incorrect? 0 answers 50 views Which of the following statements is incorrect?Which of the following statements is incorrect? &nbsp; A. If c \neq 0 and \left(a_{n}\right) converges, then \left(c a_{n}\right) converges. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The series  \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}}  0 answers 42 views The series  \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}} The series  \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}}  A. is a convergent geometric series with \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0. 0 answers 68 views Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0.Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Decide (with reasons) if the following series converge or diverge. \sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19} 0 answers 47 views Decide (with reasons) if the following series converge or diverge. \sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19}Decide (with reasons) if the following series converge or diverge. \sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Decide (with reasons) if the following series converge or diverge.\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n} 0 answers 40 views Decide (with reasons) if the following series converge or diverge.\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n}Decide (with reasons) if the following series converge or diverge.\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The series  \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}}  0 answers 53 views The series  \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}} The series  \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1}}  A. is a convergent geometric series with \sum_{n=0}^{\infty}(-1)^{n} \frac{5}{3^{n+1} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Using the geometric series \frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots, it follows that \frac{1}{1+x^{3}} has the power series expansion 0 answers 50 views Using the geometric series \frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots, it follows that \frac{1}{1+x^{3}} has the power series expansionUsing the geometric series \frac{1}{1-x}=1+x+x^{2}+x^{3}+\ldots, it follows that \frac{1}{1+x^{3}} has the power series expansion A. \quad 1+x^{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine if the following series converge \sum_{n=1}^{\infty} 3^{3 n} 7^{2-n} 0 answers 46 views Determine if the following series converge \sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}Determine if the following series converge \sum_{n=1}^{\infty} 3^{3 n} 7^{2-n} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine if the following series converge \sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}} 0 answers 47 views Determine if the following series converge \sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}Determine if the following series converge \sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that the series  \sum_{n=2}^{\infty} \dfrac{2}{n(n+1)} converges and find its limit. 0 answers 62 views Show that the series  \sum_{n=2}^{\infty} \dfrac{2}{n(n+1)} converges and find its limit.Show that the series  \sum_{n=2}^{\infty} \dfrac{2}{n(n+1)} converges and find its limit. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0. 0 answers 43 views Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0.Prove that if the series \sum_{n=1}^{\infty} a_{n} converges, then \lim _{n \rightarrow \infty} a_{n}=0. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Write down the partial fractions of \(\dfrac{x^{3}+3 x+1}{x^{2}-x-2}$
Write down the partial fractions of $\dfrac{x^{3}+3 x+1}{x^{2}-x-2}$Write down the partial fractions of $\dfrac{x^{3}+3 x+1}{x^{2}-x-2}$ ...
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Find partial fractions for the following rational functions, evaluating all constants:
Find partial fractions for the following rational functions, evaluating all constants:Find partial fractions for the following rational functions, evaluating all constants: (a) $\frac{2 x^{3}}{x^{2}-1}$ (c) \(\frac{x^{4}+x^{3}+x+1}{x^ ...
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For an infinite sheet of positive charge, the electric field lines:
For an infinite sheet of positive charge, the electric field lines:For an infinite sheet of positive charge, the electric field lines: w) run parallel to the sheet of charge x) are perpendicular to the sheet of char ...
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What is the generalized mean inequality ?
What is the generalized mean inequality ?What is the generalized mean inequality ? ...
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What are the terms used in a geometric progression?
What are the terms used in a geometric progression?What are the terms used in a geometric progression? ...
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What is the geometric progression formula?
What is the geometric progression formula?What is the geometric progression formula? ...
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What is geometric progression?
What is geometric progression?What is geometric progression? ...
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How do you find the common ratio in a geometric progression?
How do you find the common ratio in a geometric progression?How do you find the common ratio in a geometric progression? ...
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What is the sum of infinite geometric progression?
What is the sum of infinite geometric progression?What is the sum of infinite geometric progression? ...
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How do you define infinite limits in calculus?
How do you define infinite limits in calculus?How do you define infinite limits in calculus? ...
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Determine whether each of the following sets is countable or uncountable.
Determine whether each of the following sets is countable or uncountable.Determine whether each of the following sets is countable or uncountable. a. $A=\{x \in \mathbb{Q} \mid-100 \leq x \leq 100\}$ b. \$B=\{(x, y) \mid x ...
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Are there any guidelines for deciding whether an infinite set is countable or not?
Are there any guidelines for deciding whether an infinite set is countable or not?Are there any guidelines for deciding whether an infinite set is countable or not? ...
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What is the difference between countable and uncountable infinite sets?
What is the difference between countable and uncountable infinite sets?What is the difference between countable and uncountable infinite sets? ...
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What is an infinite limit in calculus?
What is an infinite limit in calculus?What is an infinite limit in calculus? ...
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Write the definition of finite sequence and infinite sequence