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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: \[ \sum_{k=4}^{7} 2 k \]
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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 \(S_{n}>300\)
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Consider the arithmetic series \((-1)+\left(\frac{-3}{2}\right)+(-2)+\cdots+(-16)\).
1 answer 67 views
Consider the arithmetic series \((-1)+\left(\frac{-3}{2}\right)+(-2)+\cdots+(-16)\).Consider the arithmetic series \((-1)+\left(\frac{-3}{2}\right)+(-2)+\cdots+(-16)\)   a) Determine the number of terms in this series. b) Calcu ...
by MathsGee Platinum
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asked in Mathematics Apr 8
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What are the applications of integrals?
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What are the applications of integrals?What are the applications of integrals? ...
by Pieter Gold Status
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asked in Mathematics Mar 31
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What are infinite integrals?
1 answer 67 views
What are infinite integrals?What are infinite integrals? ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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What is an infinite determinant?
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What is an infinite determinant?What is an infinite determinant? ...
by MathsGee Platinum
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asked in Mathematics Feb 20
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Which of the following statements is NOT TRUE?
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Which of the following statements is NOT TRUE?Which of the following statements is NOT TRUE?   (A) $\int_{0}^{3} \frac{1}{(x-4)^{2}} d x=\frac{3}{4}$. (B) $\int_{0}^{3} \frac{1}{(x-4)^{2}} ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Consider the series $\sum_{n=1}^{\infty} \frac{\cos (n \pi)}{n}$. Which of the following statements is TRUE?
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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?   (A) The series is not conditiona ...
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asked in Mathematics Jan 13
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Let $g(x, y)=x^{2} y+\cos y+y \sin x$, Which of the following statements is TRUE?
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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?   (A) $g_{x}=2 x y+\cos y+y \cos x$. (B) $g_{y}=2 x-\sin y+\s ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Consider the telescoping series $\sum_{r=1}^{\infty}\left(\dfrac{1}{r+2}-\frac{2}{r+1}+\dfrac{1}{r}\right)$.
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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.
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Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty} \dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}$
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Determine whether the following series converge or diverge. $\sum_{n=1}^{\infty}(-1)^{n}\left(\dfrac{n^{3}-1+n^{2} \sin n}{1+3 n^{3}}\right)^{n}$

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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 $\dfrac{1}{1+x^{2}}$
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The interval of convergence of the series $\sum_{n=1}^{\infty} \dfrac{(-1)^{n}(x+2)^{n}}{n}$ is
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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   A. $\quad(-3,-1$   B. $-3,-1$ &nbs ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Which FIVE of the following statements are TRUE?
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Which FIVE of the following statements are TRUE?Which FIVE of the following statements are TRUE?   A. The series $\sum_{n=1}^{\infty}\left(\frac{4 n-3}{3 n-4}\right)^{n}$ converges   B ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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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
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Determine whether the series $\sum_{n \geq 1} \dfrac{1}{\sqrt{n^{3}}}$ converges or diverges. Give a reason for your answer. 

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Find the sum of the series $\sum_{n \geq 2} \frac{2}{n^{2}-1}$
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Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$
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Which of the following statements is incorrect?
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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. ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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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} ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$.
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Decide (with reasons) if the following series converge or diverge. $\sum_{n=1}^{\infty}(-1)^{n} \frac{5-n+3 n^{2}}{7 n^{2}-19}$
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Decide (with reasons) if the following series converge or diverge.$\sum_{n=1}^{\infty}\left(\frac{5-n+3 n^{2}}{7 n^{2}-19}\right)^{n}$
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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} ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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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
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Determine if the following series converge $\sum_{n=1}^{\infty} 3^{3 n} 7^{2-n}$
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Determine if the following series converge $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}$
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Show that the series $ \sum_{n=2}^{\infty} \dfrac{2}{n(n+1)}$ converges and find its limit.
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Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$.
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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:
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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: (a) \(\frac{2 x^{3}}{x^{2}-1}\) (c) \(\frac{x^{4}+x^{3}+x+1}{x^ ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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For an infinite sheet of positive charge, the electric field lines:
1 answer 193 views
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 ...
by Digitized Wooden Status
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asked in Physics & Chemistry Oct 5, 2021
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What is the generalized mean inequality ?
1 answer 134 views
What is the generalized mean inequality ?What is the generalized mean inequality ? ...
by MathsGee Platinum
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asked in Mathematics Aug 17, 2021
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What are the terms used in a geometric progression?
1 answer 145 views
What are the terms used in a geometric progression?What are the terms used in a geometric progression? ...
by MathsGee Platinum
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asked in Mathematics Jun 27, 2021
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What is the geometric progression formula?
1 answer 116 views
What is the geometric progression formula?What is the geometric progression formula? ...
by MathsGee Platinum
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asked in Mathematics Jun 27, 2021
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What is geometric progression?
1 answer 98 views
What is geometric progression?What is geometric progression? ...
by MathsGee Platinum
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asked in Mathematics Jun 27, 2021
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How do you find the common ratio in a geometric progression?
1 answer 212 views
How do you find the common ratio in a geometric progression?How do you find the common ratio in a geometric progression? ...
by MathsGee Platinum
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asked in Mathematics Jun 27, 2021
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What is the sum of infinite geometric progression?
1 answer 133 views
What is the sum of infinite geometric progression?What is the sum of infinite geometric progression? ...
by MathsGee Platinum
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asked in Mathematics Jun 27, 2021
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How do you define infinite limits in calculus?
1 answer 105 views
How do you define infinite limits in calculus?How do you define infinite limits in calculus? ...
by Maths Genie Bronze Status
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asked in Mathematics Jun 20, 2021
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Determine whether each of the following sets is countable or uncountable.
1 answer 560 views
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 ...
by Student SIlver Status
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asked in Mathematics May 22, 2021
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Are there any guidelines for deciding whether an infinite set is countable or not?
1 answer 118 views
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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asked in Mathematics May 22, 2021
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What is the difference between countable and uncountable infinite sets?
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What is an infinite limit in calculus?
1 answer 121 views
What is an infinite limit in calculus?What is an infinite limit in calculus? ...
by MathsGee Platinum
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asked in Mathematics May 10, 2021
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Write the definition of finite sequence and infinite sequence
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Write the definition of finite sequence and infinite sequenceWrite the definition of finite sequence and infinite sequence ...
by MathsGee Platinum
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asked in Mathematics Apr 4, 2021
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Are there an infinite number of prime numbers?
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Are there an infinite number of prime numbers?Are there an infinite number of prime numbers? ...
by MathsGee Platinum
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asked in Mathematics Jan 24, 2021
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