Question

If $\sum_{n=1}^\infty x_n$ converges to s, and $y_n = \frac{x_n + x_{n+1}}{2}$ for all $n$, does $\sum_{n=1}^\infty y_n$ converge?

score 40 · Answer 1 · 2019-02-10 17:09:40

If $\sum_{n=1}^\infty x_n$ converges to s, and $y_n = \frac{x_n + x_{n+1}}{2}$ for all $n$, does $\sum_{n=1}^\infty y_n$ converge?

score 43 · Answer 2 · 2026-04-13 02:33:20

43

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score 53 · Answer 3 · 2026-04-10 14:04:25

53

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score 67 · Answer 4 · 2026-03-29 21:54:06

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score 29 · Answer 5 · 2019-02-11 09:54:04

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score 51 · Answer 6 · 2026-04-11 08:42:28

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score 46 · Answer 7 · 2026-04-13 03:00:14

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score 59 · Answer 8 · 2026-04-12 19:40:06

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score 29 · Answer 9 · 2026-04-09 17:11:07

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score 254 · Answer 10 · 2019-02-11 18:55:06

254

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score 76 · Answer 11 · 2026-04-12 02:54:05

76

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Is a completely regular space whose convergent sequences are eventually constant discrete?

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score 332 · Answer 12 · 2026-04-11 13:16:41

332

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What is the limit of the series (summation) of the q-Pochhammer symbol or the ~q-Pochhammer symbol?

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score 76 · Answer 13 · 2026-04-03 05:51:59

76

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Chose $a_n$ so that $\frac{M_n}{a_n}$ converges to 0 in distribution

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score 47 · Answer 14 · 2026-04-11 15:55:11

47

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Nested interestection forms neighbourhood basis

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score 256 · Answer 15 · 2026-03-29 21:55:23

256

Views

Uniform convergence of $\sum\limits_{n=1}^{+\infty} \left(\sin{{1} \over {n}}\right) x^n$

Published on 29 Mar 2026 - 21:55

List Question

If $\sum_{n=1}^\infty x_n$ converges to s, and $y_n = \frac{x_n + x_{n+1}}{2}$ for all $n$, does $\sum_{n=1}^\infty y_n$ converge?

For each of the statements below, prove the result if it is true, give a counter example if it is not true

limiting distribution of Xbar considering an autoregressive process

Uniform convergence of series of functions given convergence of coefficients

Convergent sequence such that its components doesn't converge to the components of the limit

Showing that a series is convergent having it as an integral

Discussing the convergence of a sequence

Computing terms of a sequence and proving it's convergent

Iterating a sequence and verifying its convergence

Studying the convergence of the series $\sqrt{2}+\sqrt{2+\sqrt{2}}+\sqrt{2+\sqrt{2+\sqrt{2}}}+ \cdots$

Is a completely regular space whose convergent sequences are eventually constant discrete?

What is the limit of the series (summation) of the q-Pochhammer symbol or the ~q-Pochhammer symbol?

Chose $a_n$ so that $\frac{M_n}{a_n}$ converges to 0 in distribution

Nested interestection forms neighbourhood basis

Uniform convergence of $\sum\limits_{n=1}^{+\infty} \left(\sin{{1} \over {n}}\right) x^n$

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