Question

Proving that show that $(f_n)_n$ admits a subsequence that simply converges on $\Bbb R$.

score 88 · Answer 1 · 2026-04-14 18:23:54

88

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Proving that show that $(f_n)_n$ admits a subsequence that simply converges on $\Bbb R$.

Published on 14 Apr 2026 - 18:23

score 3.4k · Answer 2 · 2026-04-13 16:20:17

3.4k

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Series: Finding the area of infinitely many triangles

Published on 13 Apr 2026 - 16:20

score 2.7k · Answer 3 · 2026-04-20 08:32:55

2.7k

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Find the the coefficient of $\,x^r\,$ in $\,(1+x+x^2)^n$

Published on 20 Apr 2026 - 8:32

score 53 · Answer 4 · 2026-04-15 21:13:36

53

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Finding an explicit formula for $a_n$ defined recursively by $a_{n+1}=2a_n\frac{(n+2)}{n+1} $

Published on 15 Apr 2026 - 21:13

score 138 · Answer 5 · 2026-04-13 20:02:18

138

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The convergence of a recursive sequence

Published on 13 Apr 2026 - 20:02

score 92 · Answer 6 · 2026-04-24 00:56:24

92

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Determine the limit of $\frac1n \sum\limits_{i=1}^n i^\frac{1}{i}$ as ${n \to \infty}$ .

Published on 24 Apr 2026 - 0:56

score 148 · Answer 7 · 2026-04-08 16:22:19

148

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Proof explanation: Convergence of a series

Published on 08 Apr 2026 - 16:22

score 1.1k · Answer 8 · 2026-04-16 12:10:54

1.1k

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Theorem 3.4.11 in Bartle & Sherbert's INTRO TO REAL ANALYSIS, 4th ed: Limit superior and limit inferior of a bounded sequence of real numbers

Published on 16 Apr 2026 - 12:10

score 28 · Answer 9 · 2026-04-14 06:54:33

28

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Limit of the sequence which depends on another sequence

Published on 14 Apr 2026 - 6:54

score 111 · Answer 10 · 2026-04-16 06:23:41

111

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What can we say about the series: $-1+1-1+1-1+1-1+\cdots=\sum_{n=1}^{\infty}(-1)^n$?

Published on 16 Apr 2026 - 6:23

score 156 · Answer 11 · 2026-04-16 03:12:19

156

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Need to prove: $\sum_{n=1}^{\infty}{a_n}$ converges $\implies\sum_{n=1}^{\infty }\frac{\sqrt{a_n}}{n}$ converges

Published on 16 Apr 2026 - 3:12

score 1.6k · Answer 12 · 2026-04-10 08:56:27

1.6k

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Show convergence by using partial fractions

Published on 10 Apr 2026 - 8:56

score 86 · Answer 13 · 2026-04-15 22:24:07

86

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A sequence $p_n(x)$ that converges for infinitely many values of $x$

Published on 15 Apr 2026 - 22:24

score 192 · Answer 14 · 2026-04-16 07:24:26

192

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Proof for this identity: $\sum\limits_{k=0}^\infty(\zeta(2k+3)-1) = \frac{1}{4}$

Published on 16 Apr 2026 - 7:24

score 4.7k · Answer 15 · 2026-04-12 09:59:19

4.7k

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Alternating Series Test Proof

Published on 12 Apr 2026 - 9:59

List Question

Proving that show that $(f_n)_n$ admits a subsequence that simply converges on $\Bbb R$.

Series: Finding the area of infinitely many triangles

Find the the coefficient of $\,x^r\,$ in $\,(1+x+x^2)^n$

Finding an explicit formula for $a_n$ defined recursively by $a_{n+1}=2a_n\frac{(n+2)}{n+1} $

The convergence of a recursive sequence

Determine the limit of $\frac1n \sum\limits_{i=1}^n i^\frac{1}{i}$ as ${n \to \infty}$ .

Proof explanation: Convergence of a series

Theorem 3.4.11 in Bartle & Sherbert's INTRO TO REAL ANALYSIS, 4th ed: Limit superior and limit inferior of a bounded sequence of real numbers

Limit of the sequence which depends on another sequence

What can we say about the series: $-1+1-1+1-1+1-1+\cdots=\sum_{n=1}^{\infty}(-1)^n$?

Need to prove: $\sum_{n=1}^{\infty}{a_n}$ converges $\implies\sum_{n=1}^{\infty }\frac{\sqrt{a_n}}{n}$ converges

Show convergence by using partial fractions

A sequence $p_n(x)$ that converges for infinitely many values of $x$

Proof for this identity: $\sum\limits_{k=0}^\infty(\zeta(2k+3)-1) = \frac{1}{4}$

Alternating Series Test Proof

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