Recent questions tagged sum

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Is it true that the product of any number multiplied by 9 has a sum which is a multiply of 9?
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Assume ${\{x_n\}_{n\in\mathbb{N}}}$ is a Cauchy sequence in a metric space X, and there exists a subsequence ${\{x_{n_k}\}_{k\in\mathbb{N}}}$ that converges to $x \in X$...
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Suppose that $f$ is an entire function, and$$ | f(z) | \leq A + B|z|^k$$for all $z$, where $A, B, k$ are positive real numbers. Prove that $f$ must be polynomial.
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Let $\{ x_i \}_{i=1}^n \subset \mathbb{R}^D$. Define $F: \mathbb{R}^D \to [0,\infty)$ via:$$ F(y) = \sum_{i=1}^n \Vert x_i - y \Vert_2^2$$Prove that $F$ attains a minimum...
103
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Find all pairs of consecutive odd positive integers, both of which are smaller than 18, such that their sum is more than 20.
163
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What is the sum of odd natural numbers?
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What is the palindrome of 66?
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Prove that if the series $\sum_{n=1}^{\infty} a_{n}$ converges, then $\lim _{n \rightarrow \infty} a_{n}=0$
139
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Which is the smallest?(a) -1,(b) -1/2,(c) 0,(d) 3.
221
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How do I calculate the perimeter of a regular pentagon?
243
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Consider the following quadratic number pattern: \( 6 ; 10 ; 18 ; \ldots \ldots \)1. Write down the following two terms of the pattern.2. Determine the equation of the ge...
146
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What is a regular polygon?
215
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Evaluate \(9^{\frac{ 150}{300}}\)
191
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How do I add custom shapes to Eliminator?
385
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What is the total sum of all three-digit numbers that are divisible by 7?
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The sum of the squares of three consecutive even numbers is 308. What are the integers? use latex
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The sum of three numbers is 96 . The first number is 6 times the third number, and the third number is 40 less than the second number. What is the absolute value of the d...
260
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Is pi an irrational number?
424
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Who discovered pi?
658
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How do I declare the lump sum payment to SARS as part of a severance package?
303
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Who discovered this equation \( e^{i \pi}+1=0 \)?
298
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What is the formula for the sum of first \(n\) numbers in a geometric progression?
495
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What is an irrational number?
327
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\(8 ; 24 ; 72 ; \ldots \ldots\)a) Write down the next 3 terms of the sequence.b) Find the general term.c) Show by calculation whether 5832 is a term of this sequence or n...
438
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In an arithmetic sequence \(S_n=n^2-2 n\). Use your formula in 2 to determine the value of:(a) \(\mathrm{T}_7\)(b) \(\mathrm{T}_{50}\)(c) \(\mathrm{T}_n\)
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Consider the geometric sequence: \(\quad 8 x^2 ; 4 x^3 ; 2 x^4 ; \ldots \ldots \ldots\)(a) Show that the general term is given by \(\mathrm{T}_n=2^{4-n} \cdot x^{1+n}\)(b...
448
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What is the greatest value of \(p\) for which the series \(\sum_{k=1}^p 10(3)^{k-1}<2300\) ?
372
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Calculate the difference between \(S_{\infty}\) and \(S_7\) of \(4+\frac{4}{3}+\frac{4}{9}+\ldots\)
354
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Write each of the following series in sigma notation:(a) \(1+4+7+\ldots .+70\)(b) \(1-1-3-\ldots . .-111\)(c) \(1+\frac{1}{2}+\frac{1}{4}+\ldots\)(d) \(2-6+18-54+\ldots ....
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The sum to infinity of a convergent geometric series is 32 and \(r=\frac{1}{2}\). Find the difference between the sum to infinity and the sum of the first five terms.
348
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Calculate: \(\quad \sum_{n=1}^{\infty} 2.10^{1-n} \quad\) (if it exists)
277
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Calculate the sum to infinity of the geometric series \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\ldots .\).
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Prove that in a convergent geometric series in which \(-1<r<1\), the sum to infinity is given by the formula: \(S_{\infty}=\dfrac{a}{1-r}\)
324
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If \(\mathrm{T}_3=\frac{15}{16}, \mathrm{~T}_6=\frac{5}{18}\) and the last term is \(\frac{40}{729}\), find the number of terms in the sequence if the sequence is geometr...
372
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Given is the series \(1+2+3+4+5+\ldots .+n\)(a) Show that \(\mathrm{S}_n=\frac{n(n+1)}{2}\).(b) Find the sum of the first 1001 terms excluding all multiples of 7.
229
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What is the least value of \(p\) for which the series \(\sum_{k=1}^p \frac{1}{16}(2)^{k-2}>31\) ?
377
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Determine \(n\) if: \(3+6+12+\ldots\) (to \(n\) terms) \(=765\)
209
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How many terms of the geometric sequence \(\frac{1}{27} ; \frac{1}{9} ; \frac{1}{3} ; \ldots\)
394
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How many terms of the geometric sequence \(64 ; 32 ; 16 ; \ldots\) will add up to \(127 \frac{1}{2}\) ?
366
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Calculate \(\sum_{i=0}^{10} 3^{4-i}\)
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Evaluate: \(-9-6-4-\ldots .-1 \frac{5}{27}\)
423
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How many terms are there in the series \(-64-32-16-\ldots .-\frac{1}{32}\). What is the sum of the series?
246
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Determine the sum of each geometric series (use an appropriate formula):(a) \(\frac{2}{27}+\frac{2}{9}+\frac{2}{3}+\ldots\) to 9 terms(b) \(-64+32-16+\ldots\) to 10 terms...
259
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How many terms of the geometric sequence \(-1 ; 2 ;-4 ; 8 ; \ldots\). will add up to \(349525 ?\)
323
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Find the sum of the first 12 terms of the series \(\dfrac{2}{3}+2+6+\ldots\)
281
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Prove that the sum of the first \(n\) terms of a geometric sequence is given by the formula \(\mathrm{S}_n=\dfrac{a\left(r^n-1\right)}{r-1}\) where \(r \neq 1 \quad\) or ...
178
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Evaluate the geometric series: \(S_6=4+12+36+108+324+972\)
438
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Which formula do we use to calculate the sum of a finite geometric series?
374
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How many terms of the arithmetic sequence \(4 ; 7 ; 10 ; 13 ; \ldots\) will add up to 175 ?
213
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Calculate \(\sum_{m=2}^{100}(7-2 m)\)
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