Question

Show $\lim_{n\to \infty} 2^n-(2+\frac{1}{n})^n = -\infty$

score 75 · Answer 1 · 2026-04-16 11:27:52

75

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Show $\lim_{n\to \infty} 2^n-(2+\frac{1}{n})^n = -\infty$

Published on 16 Apr 2026 - 11:27

score 43 · Answer 2 · 2026-04-12 02:46:18

43

Views

Inductive formula involving parity

Published on 12 Apr 2026 - 2:46

score 164 · Answer 3 · 2026-04-15 00:22:27

164

Views

What's the nonstandard way to argue $\lim_{n\to\infty}\sum_{k=0}^n\binom n k (\frac x n)^k = \sum_{k=0}^\infty \frac{x^k}{k!}$

Published on 15 Apr 2026 - 0:22

score 87 · Answer 4 · 2026-04-16 19:29:01

87

Views

How to prove that generating function of series ($1 ,\binom{m}{1},\binom{m+1}{2},\binom{m+2}{3},...$ ) equals $\frac{1}{(1-z)^m}$ .

Published on 16 Apr 2026 - 19:29

score 319 · Answer 5 · 2026-04-11 23:03:21

319

Views

Counting measure and inclusion of $\mathcal{L}_p$ spaces.

Published on 11 Apr 2026 - 23:03

score 81 · Answer 6 · 2026-04-12 01:25:53

81

Views

How the function $f_n$ is a measurable function?

Published on 12 Apr 2026 - 1:25

score 1.3k · Answer 7 · 2026-04-14 13:42:25

1.3k

Views

Is $f(x)=\frac{\cos x}x$ uniformly continuous in $(0,1)$?

Published on 14 Apr 2026 - 13:42

score 205 · Answer 8 · 2026-04-29 12:42:56

205

Views

Prove that $\lim\limits_{n\to\infty}\frac{1}{n}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}\right)=0$

Published on 29 Apr 2026 - 12:42

score 156 · Answer 9 · 2026-04-17 06:36:22

156

Views

The general term of $\frac{2^2}{5!}-\frac{5^7}{6!}+\frac{8^{12}}{7!}-\frac{11^{17}}{8!}+\cdots$

Published on 17 Apr 2026 - 6:36

score 103 · Answer 10 · 2026-04-16 00:59:38

103

Views

$\lim_{n\to\infty}\int f_n =0$ while $\limsup_{n\to\infty} f_n = +\infty$

Published on 16 Apr 2026 - 0:59

score 323 · Answer 11 · 2026-04-15 15:36:38

323

Views

Example of series such that $\sum a_n$ is divergent but $\sum \frac{ a_n}{1+ n a_n}$ is convergent

Published on 15 Apr 2026 - 15:36

score 45 · Answer 12 · 2026-04-17 03:11:18

45

Views

What is the minimial polynomial of $1+(v_{p_i}(p_j-1))_{1 \le i,j \le n}$?

Published on 17 Apr 2026 - 3:11

score 98 · Answer 13 · 2026-04-16 12:44:08

98

Views

How do I prove that $\sum_{i=1}^m \cos^2\left(\frac{2\pi i}{m}\right) = \sum_{i=1}^m \sin^2\left(\frac{2\pi i}{m}\right) = \frac{m}{2}$?

Published on 16 Apr 2026 - 12:44

score 608 · Answer 14 · 2026-04-17 14:11:01

608

Views

If $(X_n)$ are i.i.d random variables, then $P(X_1\geq 0)=1$ and $P(X_1 >0)>0$ implies $\sum X_n =\infty$

Published on 17 Apr 2026 - 14:11

score 90 · Answer 15 · 2026-04-16 14:05:21

90

Views

Show that $\sum_{n=0}^\infty\frac{1}{(2n+1)3^{2n+1}}=$ ln$(\sqrt2)$

Published on 16 Apr 2026 - 14:05

List Question

Show $\lim_{n\to \infty} 2^n-(2+\frac{1}{n})^n = -\infty$

Inductive formula involving parity

What's the nonstandard way to argue $\lim_{n\to\infty}\sum_{k=0}^n\binom n k (\frac x n)^k = \sum_{k=0}^\infty \frac{x^k}{k!}$

How to prove that generating function of series ($1 ,\binom{m}{1},\binom{m+1}{2},\binom{m+2}{3},...$ ) equals $\frac{1}{(1-z)^m}$ .

Counting measure and inclusion of $\mathcal{L}_p$ spaces.

How the function $f_n$ is a measurable function?

Is $f(x)=\frac{\cos x}x$ uniformly continuous in $(0,1)$?

Prove that $\lim\limits_{n\to\infty}\frac{1}{n}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}\right)=0$

The general term of $\frac{2^2}{5!}-\frac{5^7}{6!}+\frac{8^{12}}{7!}-\frac{11^{17}}{8!}+\cdots$

$\lim_{n\to\infty}\int f_n =0$ while $\limsup_{n\to\infty} f_n = +\infty$

Example of series such that $\sum a_n$ is divergent but $\sum \frac{ a_n}{1+ n a_n}$ is convergent

What is the minimial polynomial of $1+(v_{p_i}(p_j-1))_{1 \le i,j \le n}$?

How do I prove that $\sum_{i=1}^m \cos^2\left(\frac{2\pi i}{m}\right) = \sum_{i=1}^m \sin^2\left(\frac{2\pi i}{m}\right) = \frac{m}{2}$?

If $(X_n)$ are i.i.d random variables, then $P(X_1\geq 0)=1$ and $P(X_1 >0)>0$ implies $\sum X_n =\infty$

Show that $\sum_{n=0}^\infty\frac{1}{(2n+1)3^{2n+1}}=$ ln$(\sqrt2)$

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