Question

Can we say that, for any $n\in\mathbb {R^{+}}$ following inequality is correct?

score 66 · Answer 1 · 2026-04-15 01:27:02

66

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Can we say that, for any $n\in\mathbb {R^{+}}$ following inequality is correct?

Published on 15 Apr 2026 - 1:27

score 107 · Answer 2 · 2026-04-14 06:31:47

107

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To what number does $ n^{-2} \times \sum_{m=1}^{n-1} n \bmod m$ converge, as $n$ gets large?

Published on 14 Apr 2026 - 6:31

score 952 · Answer 3 · 2026-04-17 00:33:03

952

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Evaluate $\lim\limits_{n\rightarrow \infty}\frac{n+n^2+n^3+\cdots +n^n}{1^n+2^n+3^n+\cdots +n^n}.$

Published on 17 Apr 2026 - 0:33

score 1k · Answer 4 · 2026-04-14 17:43:26

1k

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Limit of $\dfrac{e^{-1/|x|}}{x^n}$ as $x\to 0$

Published on 14 Apr 2026 - 17:43

score 58 · Answer 5 · 2026-04-17 08:15:43

58

Views

Find the big-O of the sequence $a_{0} = a_{1} = 1, a_{n} = 2a_{n - 1} - 2a_{n - 2}$

Published on 17 Apr 2026 - 8:15

score 445 · Answer 6 · 2026-04-13 14:47:01

445

Views

Use the precise definition to prove $\lim_{x \to 1} \frac{x}{x-1} = \infty$.

Published on 13 Apr 2026 - 14:47

score 37 · Answer 7 · 2026-04-10 17:20:55

37

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how fast decrease a limit

Published on 10 Apr 2026 - 17:20

score 130 · Answer 8 · 2026-04-14 06:24:40

130

Views

Alternative proof limit definition is equivalent to sequence limit definition (Rudin 4.2)

Published on 14 Apr 2026 - 6:24

score 138 · Answer 9 · 2026-04-15 03:51:51

138

Views

How to solve the diffencial equation for power series $(1+x²)y'' - 6xy=0$ in $x_{0}=0$

Published on 15 Apr 2026 - 3:51

score 99 · Answer 10 · 2026-04-25 11:50:50

99

Views

Evaluating $\lim_{(x,y) \to (\pi,0)} {\cos(x) + 1 + {y^2/2} \over (x - \pi)^2 + y^2}$

Published on 25 Apr 2026 - 11:50

score 1k · Answer 11 · 2026-04-14 15:44:00

1k

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Limit of the ratio of two modified Bessel functions

Published on 14 Apr 2026 - 15:44

score 41 · Answer 12 · 2026-04-15 03:37:26

41

Views

Limit of $-1+i\frac{(-1)^n}{n^2}$ in Polar Coordinates

Published on 15 Apr 2026 - 3:37

score 155 · Answer 13 · 2026-04-17 04:59:22

155

Views

Why doesn't $\lim_\limits{x\to\infty} f(x) = 0$ directly imply $\lim_\limits{x\to\infty}f'(x) = 0$

Published on 17 Apr 2026 - 4:59

score 75 · Answer 14 · 2026-04-16 04:48:11

75

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Compute $\lim_{x\to\infty}x-\sqrt{x^2+x+1}\frac {\ln(e^x+x)}{x}$

Published on 16 Apr 2026 - 4:48

score 282 · Answer 15 · 2026-04-18 13:50:15

282

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How to evaluate the limit $\int_{0}^{\frac{\pi}{2}}Re^{-R\sin\theta}d\theta \quad (\text{as } R \rightarrow \infty)$

Published on 18 Apr 2026 - 13:50

List Question

Can we say that, for any $n\in\mathbb {R^{+}}$ following inequality is correct?

To what number does $ n^{-2} \times \sum_{m=1}^{n-1} n \bmod m$ converge, as $n$ gets large?

Evaluate $\lim\limits_{n\rightarrow \infty}\frac{n+n^2+n^3+\cdots +n^n}{1^n+2^n+3^n+\cdots +n^n}.$

Limit of $\dfrac{e^{-1/|x|}}{x^n}$ as $x\to 0$

Find the big-O of the sequence $a_{0} = a_{1} = 1, a_{n} = 2a_{n - 1} - 2a_{n - 2}$

Use the precise definition to prove $\lim_{x \to 1} \frac{x}{x-1} = \infty$.

how fast decrease a limit

Alternative proof limit definition is equivalent to sequence limit definition (Rudin 4.2)

How to solve the diffencial equation for power series $(1+x²)y'' - 6xy=0$ in $x_{0}=0$

Evaluating $\lim_{(x,y) \to (\pi,0)} {\cos(x) + 1 + {y^2/2} \over (x - \pi)^2 + y^2}$

Limit of the ratio of two modified Bessel functions

Limit of $-1+i\frac{(-1)^n}{n^2}$ in Polar Coordinates

Why doesn't $\lim_\limits{x\to\infty} f(x) = 0$ directly imply $\lim_\limits{x\to\infty}f'(x) = 0$

Compute $\lim_{x\to\infty}x-\sqrt{x^2+x+1}\frac {\ln(e^x+x)}{x}$

How to evaluate the limit $\int_{0}^{\frac{\pi}{2}}Re^{-R\sin\theta}d\theta \quad (\text{as } R \rightarrow \infty)$

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