Question

How can we show that $ (a_n), (b_n), (c_n) $ are convergent and have the same limit?

score 255 · Answer 1 · 2026-03-25 17:21:39

255

Views

How can we show that $ (a_n), (b_n), (c_n) $ are convergent and have the same limit?

Published on 25 Mar 2026 - 17:21

score 253 · Answer 2 · 2026-04-01 01:18:25

253

Views

Find limit of $\lim_{x\to 0}\frac{\sin^{200}(x)}{x^{199}\sin(4x)}$, if it exists

Published on 01 Apr 2026 - 1:18

score 176 · Answer 3 · 2026-03-25 08:10:00

176

Views

Computing $\lim\limits_{n\to \infty}\frac1n\left((n+1)(n+2)...(n+n)\right)^{\frac1n}$

Published on 25 Mar 2026 - 8:10

score 66 · Answer 4 · 2026-04-10 22:14:56

66

Views

Clearest definition of a limit

Published on 10 Apr 2026 - 22:14

score 115 · Answer 5 · 2026-03-25 17:21:55

115

Views

On uniform convergence of $f_n(x) = (2^n +|x|^n)^{1/n}$ for $x\in \mathbb{R}$

Published on 25 Mar 2026 - 17:21

score 84 · Answer 6 · 2026-03-25 17:21:39

84

Views

show that $\sum_{k=1}^{\infty}{\left ( \frac{1}{2} + \frac{1}{k}\right )^k}$ converges

Published on 25 Mar 2026 - 17:21

score 290 · Answer 7 · 2026-03-25 08:13:40

290

Views

How to calculate the limit $\lim _{n\to \infty }\sum _{k=1}^n\sqrt{n^4+k}\sin(\frac{2k\pi }{n})$? Is it a Riemann sum?

Published on 25 Mar 2026 - 8:13

score 47 · Answer 8 · 2026-04-09 07:00:45

47

Views

trigonometry limit finding using squeeze thereom didn't work out

Published on 09 Apr 2026 - 7:00

score 72 · Answer 9 · 2018-02-06 14:36:21

72

Views

$\lim_{x\to \infty}{\frac{4^{x+1} + 3^{x-2} + 2^{x+1}}{4^{x-1} + 3^{x+1} + 2^{x-1}}}$

Published on 06 Feb 2018 - 14:36

score 36 · Answer 10 · 2018-02-06 15:46:49

How to find the limit of $\lim_{n\rightarrow\infty}\frac{[\sum_{i=0}^{n} (2i+1)^\alpha]^{\beta+1}}{[\sum_{i=1}^{n} (2i)^\beta]^{\alpha+1}}$?

score 86 · Answer 11 · 2026-04-07 01:43:15

86

Views

check if $\sum_{k=1}^{\infty}{ \left( \frac{7k-2}{8k-3 \sqrt{k}}\right)}^k$ converges

Published on 07 Apr 2026 - 1:43

score 93 · Answer 12 · 2026-03-26 06:05:37

93

Views

Proof verification: show that $\lim_{x\to 1}\frac{1}{e^{x-1}}$ does not exist.

Published on 26 Mar 2026 - 6:05

score 677 · Answer 13 · 2026-04-11 23:54:49

677

Views

How to find $\lim\limits _{n\to \infty }(n[\frac{5}{n}])$

Published on 11 Apr 2026 - 23:54

score 27 · Answer 14 · 2018-02-06 19:44:38

27

Views

Property of sequences in $\mathbb{R}^N$

Published on 06 Feb 2018 - 19:44

score 52 · Answer 15 · 2026-04-09 00:33:34

52

Views

Understanding the definition of a limit using neighborhoods in $R^1$ (Rudin)

Published on 09 Apr 2026 - 0:33

List Question

How can we show that $ (a_n), (b_n), (c_n) $ are convergent and have the same limit?

Find limit of $\lim_{x\to 0}\frac{\sin^{200}(x)}{x^{199}\sin(4x)}$, if it exists

Computing $\lim\limits_{n\to \infty}\frac1n\left((n+1)(n+2)...(n+n)\right)^{\frac1n}$

Clearest definition of a limit

On uniform convergence of $f_n(x) = (2^n +|x|^n)^{1/n}$ for $x\in \mathbb{R}$

show that $\sum_{k=1}^{\infty}{\left ( \frac{1}{2} + \frac{1}{k}\right )^k}$ converges

How to calculate the limit $\lim _{n\to \infty }\sum _{k=1}^n\sqrt{n^4+k}\sin(\frac{2k\pi }{n})$? Is it a Riemann sum?

trigonometry limit finding using squeeze thereom didn't work out

$\lim_{x\to \infty}{\frac{4^{x+1} + 3^{x-2} + 2^{x+1}}{4^{x-1} + 3^{x+1} + 2^{x-1}}}$

How to find the limit of $\lim_{n\rightarrow\infty}\frac{[\sum_{i=0}^{n} (2i+1)^\alpha]^{\beta+1}}{[\sum_{i=1}^{n} (2i)^\beta]^{\alpha+1}}$?

check if $\sum_{k=1}^{\infty}{ \left( \frac{7k-2}{8k-3 \sqrt{k}}\right)}^k$ converges

Proof verification: show that $\lim_{x\to 1}\frac{1}{e^{x-1}}$ does not exist.

How to find $\lim\limits _{n\to \infty }(n[\frac{5}{n}])$

Property of sequences in $\mathbb{R}^N$

Understanding the definition of a limit using neighborhoods in $R^1$ (Rudin)

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