Question

Determine divergence or convergence of $\sum_{n=1}^\infty \frac{\cos\frac{\pi}{4n}}{\sqrt[5]{2n^5-1}}$

score 76 · Answer 1 · 2018-10-20 16:33:23

76

Views

Determine divergence or convergence of $\sum_{n=1}^\infty \frac{\cos\frac{\pi}{4n}}{\sqrt[5]{2n^5-1}}$

Published on 20 Oct 2018 - 16:33

score 194 · Answer 2 · 2018-10-20 18:30:49

194

Views

Given that $\{a_n\}$ is a sequence of $\mathbb{R}$ s.t. $a_n \leq b_n$ and $a_n \rightarrow a$ and $b_n \rightarrow b$ then $a \leq b$

Published on 20 Oct 2018 - 18:30

score 38 · Answer 3 · 2018-10-20 19:20:41

38

Views

limit when $\lim \limits _{n \to \infty} \sum _{i=0} ^{n} \frac{1}{2^i}$

Published on 20 Oct 2018 - 19:20

score 135 · Answer 4 · 2026-03-28 09:33:32

135

Views

For which real $a$ does$ \sum_{n=1}^{\infty} \left\{ e-\left(1+\frac{1}{n}\right)^{n+a} \right\}$ converge or diverge?

Published on 28 Mar 2026 - 9:33

score 68 · Answer 5 · 2018-10-21 14:53:39

68

Views

If $\{a_n\}$ is a sequence in which $a_n \geq c$ for some constant $c$ and $a_n \rightarrow a$ then $a \geq c$

Published on 21 Oct 2018 - 14:53

score 27 · Answer 6 · 2026-03-26 11:16:44

27

Views

How does uniform continuity and continuity affect the convergence of a function

Published on 26 Mar 2026 - 11:16

score 96 · Answer 7 · 2018-10-21 19:27:09

96

Views

Prove $\lim_{n\to\infty}U_{n} = 1$ given $0 \lt U_{n} - {1\over U_{n}}\lt {1\over n}$ and $U_n>0$

Published on 21 Oct 2018 - 19:27

score 374 · Answer 8 · 2018-10-21 22:37:05

374

Views

If $\{x_n\}$ is a sequence s.t. $x_{2k} \rightarrow x$ and $x_{2k-1} \rightarrow x$, then $x_k \rightarrow x$

Published on 21 Oct 2018 - 22:37

score 44 · Answer 9 · 2018-10-22 00:50:14

44

Views

Convergence of series and limit

Published on 22 Oct 2018 - 0:50

score 84 · Answer 10 · 2018-10-22 02:14:31

84

Views

Prove that if a sequence $(a_n)$ converges to some limit $L$, then $2^{a_n}$ converges to $2^L$

Published on 22 Oct 2018 - 2:14

score 45 · Answer 11 · 2018-10-22 09:50:26

45

Views

Checking series for convergence and limit

Published on 22 Oct 2018 - 9:50

score 135 · Answer 12 · 2018-10-22 10:58:39

135

Views

About the proof that “ a bounded and monotone sequence is convergent”

Published on 22 Oct 2018 - 10:58

score 63 · Answer 13 · 2018-10-22 19:55:34

63

Views

Convergence in distribution with a convergent sequence of reals

Published on 22 Oct 2018 - 19:55

score 38 · Answer 14 · 2018-10-22 22:08:36

38

Views

Series, limits and convergence

Published on 22 Oct 2018 - 22:08

score 25 · Answer 15 · 2018-10-22 22:56:08

25

Views

sequence and series, limits

Published on 22 Oct 2018 - 22:56

List Question

Determine divergence or convergence of $\sum_{n=1}^\infty \frac{\cos\frac{\pi}{4n}}{\sqrt[5]{2n^5-1}}$

Given that $\{a_n\}$ is a sequence of $\mathbb{R}$ s.t. $a_n \leq b_n$ and $a_n \rightarrow a$ and $b_n \rightarrow b$ then $a \leq b$

limit when $\lim \limits _{n \to \infty} \sum _{i=0} ^{n} \frac{1}{2^i}$

For which real $a$ does$ \sum_{n=1}^{\infty} \left\{ e-\left(1+\frac{1}{n}\right)^{n+a} \right\}$ converge or diverge?

If $\{a_n\}$ is a sequence in which $a_n \geq c$ for some constant $c$ and $a_n \rightarrow a$ then $a \geq c$

How does uniform continuity and continuity affect the convergence of a function

Prove $\lim_{n\to\infty}U_{n} = 1$ given $0 \lt U_{n} - {1\over U_{n}}\lt {1\over n}$ and $U_n>0$

If $\{x_n\}$ is a sequence s.t. $x_{2k} \rightarrow x$ and $x_{2k-1} \rightarrow x$, then $x_k \rightarrow x$

Convergence of series and limit

Prove that if a sequence $(a_n)$ converges to some limit $L$, then $2^{a_n}$ converges to $2^L$

Checking series for convergence and limit

About the proof that “ a bounded and monotone sequence is convergent”

Convergence in distribution with a convergent sequence of reals

Series, limits and convergence

sequence and series, limits

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