Question

Find $\lim_{n\to \infty} \big[\frac{1}{1\cdot3}+\frac{1}{2\cdot5}+...+\frac{1}{n\cdot(2n+1)}\big]$

score 260 · Answer 1 · 2018-01-29 18:47:51

260

Views

Find $\lim_{n\to \infty} \big[\frac{1}{1\cdot3}+\frac{1}{2\cdot5}+...+\frac{1}{n\cdot(2n+1)}\big]$

Published on 29 Jan 2018 - 18:47

score 161 · Answer 2 · 2018-01-29 18:54:44

161

Views

How to prove that a function $f$ has a limit $l$ when $x \to x_0$, using the ε-δ definition?

Published on 29 Jan 2018 - 18:54

score 159 · Answer 3 · 2026-04-11 07:17:42

159

Views

Convergence of $(x_n)_n$ if $2018^2=x_{n+1}\sqrt[n+1]{x_1\cdot x_2\cdots x_n}$ $\forall~n$

Published on 11 Apr 2026 - 7:17

score 34 · Answer 4 · 2026-04-11 01:31:42

34

Views

Finite sum of expression as exponent goes to infinity

Published on 11 Apr 2026 - 1:31

score 89 · Answer 5 · 2018-01-29 21:45:38

89

Views

Given $\frac{1}{1^4}+\frac{1}{2^4}...\infty=\frac{\pi^4}{90}$

Published on 29 Jan 2018 - 21:45

score 186 · Answer 6 · 2026-04-06 17:12:49

186

Views

Converging series & proving that all terms are larger than a certain number

Published on 06 Apr 2026 - 17:12

score 460 · Answer 7 · 2026-04-09 12:07:02

460

Views

Prove $\lim\limits_{n \to \infty} \frac{\log (n!)}{n \sqrt[n]{\log 2 \cdot \log 3 \cdots \log n}}=1$

Published on 09 Apr 2026 - 12:07

score 70 · Answer 8 · 2018-01-30 01:30:39

70

Views

What is the limit of the serie $\sum_{k=0}^{\infty}\frac{x^4}{(1+x^2)^k}$

Published on 30 Jan 2018 - 1:30

score 69 · Answer 9 · 2026-04-11 02:59:11

69

Views

Calculus Limits

Published on 11 Apr 2026 - 2:59

score 74 · Answer 10 · 2026-03-25 12:17:25

74

Views

Proving that $a_{n} \rightarrow L$ given that $a_{n}+ 2a_{n+1} \rightarrow 3L$ .

Published on 25 Mar 2026 - 12:17

score 32 · Answer 11 · 2026-04-11 10:30:20

32

Views

how to prove that after specific value of negative power, any two exponential functions will be equal?

Published on 11 Apr 2026 - 10:30

score 135 · Answer 12 · 2026-04-09 02:02:04

135

Views

Calculate the limit $L=\lim_{x\to 0^+}\left(2\sin\left(\sqrt{x}\right)+\sqrt{x}\sin\left(\frac{1}{x}\right)\right)^x$.

Published on 09 Apr 2026 - 2:02

score 63 · Answer 13 · 2026-03-24 20:38:07

63

Views

Proving a property of a $L^1(\mu)$ function.

Published on 24 Mar 2026 - 20:38

score 211 · Answer 14 · 2026-04-11 01:28:44

211

Views

If the derivative exists when $x$ approaches a point, is $f$ differentiable at that point?

Published on 11 Apr 2026 - 1:28

score 377 · Answer 15 · 2026-03-24 22:12:42

377

Views

Epsilon-delta proof of a multivariate limit

Published on 24 Mar 2026 - 22:12

List Question

Find $\lim_{n\to \infty} \big[\frac{1}{1\cdot3}+\frac{1}{2\cdot5}+...+\frac{1}{n\cdot(2n+1)}\big]$

How to prove that a function $f$ has a limit $l$ when $x \to x_0$, using the ε-δ definition?

Convergence of $(x_n)_n$ if $2018^2=x_{n+1}\sqrt[n+1]{x_1\cdot x_2\cdots x_n}$ $\forall~n$

Finite sum of expression as exponent goes to infinity

Given $\frac{1}{1^4}+\frac{1}{2^4}...\infty=\frac{\pi^4}{90}$

Converging series & proving that all terms are larger than a certain number

Prove $\lim\limits_{n \to \infty} \frac{\log (n!)}{n \sqrt[n]{\log 2 \cdot \log 3 \cdots \log n}}=1$

What is the limit of the serie $\sum_{k=0}^{\infty}\frac{x^4}{(1+x^2)^k}$

Calculus Limits

Proving that $a_{n} \rightarrow L$ given that $a_{n}+ 2a_{n+1} \rightarrow 3L$ .

how to prove that after specific value of negative power, any two exponential functions will be equal?

Calculate the limit $L=\lim_{x\to 0^+}\left(2\sin\left(\sqrt{x}\right)+\sqrt{x}\sin\left(\frac{1}{x}\right)\right)^x$.

Proving a property of a $L^1(\mu)$ function.

If the derivative exists when $x$ approaches a point, is $f$ differentiable at that point?

Epsilon-delta proof of a multivariate limit

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