# Recent questions tagged sum

116
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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?
95
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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 $x \in X$...
71
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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.
80
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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?
82
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What is the palindrome of 66?
189
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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?
590
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The sum of the squares of three consecutive even numbers is 308. What are the integers? use latex
660
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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) $$\mathrm{T}_n$$
465
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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 .... 443 views 0 answers 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 .$$.
269
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Prove that in a convergent geometric series in which $$-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}$$
199
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Evaluate: $$-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$$
How many terms of the arithmetic sequence $$4 ; 7 ; 10 ; 13 ; \ldots$$ will add up to 175 ?
Calculate $$\sum_{m=2}^{100}(7-2 m)$$