Question

Find the limit of sequence $\frac{1}{2}+\frac{3}{2^{2}}+\frac{5}{2^{3}}+\cdots+\frac{2n-1}{2^{n}}$ without using of derivatives and etc.

score 241 · Answer 1 · 2026-04-16 19:03:27

Find the limit of sequence $\frac{1}{2}+\frac{3}{2^{2}}+\frac{5}{2^{3}}+\cdots+\frac{2n-1}{2^{n}}$ without using of derivatives and etc.

score 55 · Answer 2 · 2026-04-12 14:29:01

55

Views

Finding limit of a convergent sequence

Published on 12 Apr 2026 - 14:29

score 59 · Answer 3 · 2026-04-15 14:45:27

59

Views

Baffled with $\lim\limits_{x\to 0^+}{1+\ln^2 x\over x}$

Published on 15 Apr 2026 - 14:45

score 110 · Answer 4 · 2026-04-15 16:30:38

110

Views

Calculate the limit: $\lim\limits_{n\to\infty} a_n = \frac{1}{n^2}\sum\limits_{i=1}^ni\cdot e^\frac{i^2}{n^2}$

Published on 15 Apr 2026 - 16:30

score 82 · Answer 5 · 2026-04-16 16:24:30

82

Views

Find $\lim_{n\to \infty}\int_1^{\infty}\frac{n}{1+x^n}dx$

Published on 16 Apr 2026 - 16:24

score 753 · Answer 6 · 2026-04-14 22:45:51

753

Views

Complex limit $e^{1/z^2}$ at $z=0$

Published on 14 Apr 2026 - 22:45

score 87 · Answer 7 · 2026-04-15 16:36:27

87

Views

Is it true that $ n\sqrt{n^2-1} > \frac{n^2}{2}?$

Published on 15 Apr 2026 - 16:36

score 75 · Answer 8 · 2026-04-16 21:14:29

75

Views

Show the following limit, using the definition of epsilon-delta.

Published on 16 Apr 2026 - 21:14

score 311 · Answer 9 · 2026-04-16 10:45:46

311

Views

Find $\lim_{x\to\infty}\left( \sqrt{(x+a)(x+b)}-x \right)$ where $a,b \in \mathbb{R}$

Published on 16 Apr 2026 - 10:45

score 346 · Answer 10 · 2026-04-15 17:42:34

346

Views

Show that the sequence $a_n=\frac{cos(n^2+n)}{n^2}$ converges to $0$.

Published on 15 Apr 2026 - 17:42

score 516 · Answer 11 · 2026-04-09 03:48:50

516

Views

Limits of Power Series

Published on 09 Apr 2026 - 3:48

score 24 · Answer 12 · 2026-04-17 13:53:58

24

Views

Set of all triples making a piecewise function differentiable

Published on 17 Apr 2026 - 13:53

score 146 · Answer 13 · 2026-04-11 19:05:42

146

Views

How to solve this limit without L'Hospital's rules

Published on 11 Apr 2026 - 19:05

score 50 · Answer 14 · 2026-04-16 07:49:18

50

Views

It's correct to claim that $\lim_{n \rightarrow \infty}{\frac{f(n^k)}{f(n^{k+1})}}<1$?

Published on 16 Apr 2026 - 7:49

score 2.9k · Answer 15 · 2026-04-16 05:15:44

2.9k

Views

Evaluate $\lim_{x\rightarrow\mathrm\pi}\frac{\sin(mx)}{\sin(nx)}$

Published on 16 Apr 2026 - 5:15

List Question

Find the limit of sequence $\frac{1}{2}+\frac{3}{2^{2}}+\frac{5}{2^{3}}+\cdots+\frac{2n-1}{2^{n}}$ without using of derivatives and etc.

Finding limit of a convergent sequence

Baffled with $\lim\limits_{x\to 0^+}{1+\ln^2 x\over x}$

Calculate the limit: $\lim\limits_{n\to\infty} a_n = \frac{1}{n^2}\sum\limits_{i=1}^ni\cdot e^\frac{i^2}{n^2}$

Find $\lim_{n\to \infty}\int_1^{\infty}\frac{n}{1+x^n}dx$

Complex limit $e^{1/z^2}$ at $z=0$

Is it true that $ n\sqrt{n^2-1} > \frac{n^2}{2}?$

Show the following limit, using the definition of epsilon-delta.

Find $\lim_{x\to\infty}\left( \sqrt{(x+a)(x+b)}-x \right)$ where $a,b \in \mathbb{R}$

Show that the sequence $a_n=\frac{cos(n^2+n)}{n^2}$ converges to $0$.

Limits of Power Series

Set of all triples making a piecewise function differentiable

How to solve this limit without L'Hospital's rules

It's correct to claim that $\lim_{n \rightarrow \infty}{\frac{f(n^k)}{f(n^{k+1})}}<1$?

Evaluate $\lim_{x\rightarrow\mathrm\pi}\frac{\sin(mx)}{\sin(nx)}$

Trending Questions

Popular # Hahtags

Popular Questions