Question

Proving the existence of Pi with Derivatives and Sequences Only

score 106 · Answer 1 · 2026-04-13 08:15:46

106

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Proving the existence of Pi with Derivatives and Sequences Only

Published on 13 Apr 2026 - 8:15

score 34 · Answer 2 · 2026-04-14 05:24:54

34

Views

Uniform convergence of trigonometric integral

Published on 14 Apr 2026 - 5:24

score 177 · Answer 3 · 2026-04-16 14:50:17

177

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Convergence of $\lim\limits_{n\to\infty}\frac{1}{n}\int_\limits{-n}^{n}\frac{1-e^{-nx^2}}{x^2(1+nx^2)}dx$

Published on 16 Apr 2026 - 14:50

score 72 · Answer 4 · 2026-04-10 04:35:11

72

Views

Explicit form of a double indexed sequence

Published on 10 Apr 2026 - 4:35

score 67 · Answer 5 · 2026-04-15 09:13:17

67

Views

Positive subsequence of a double sequence

Published on 15 Apr 2026 - 9:13

score 316 · Answer 6 · 2026-04-25 21:43:45

316

Views

About digamma function, does $\psi(a) =-\sum_{n=0}^{\infty} \frac{1} {n+a} ?$

Published on 25 Apr 2026 - 21:43

score 233 · Answer 7 · 2026-04-14 22:46:51

233

Views

Compute $\lim_{n\to\infty}\int_\limits{0}^{\infty}\frac{dx}{x^{n}+1}$

Published on 14 Apr 2026 - 22:46

score 46 · Answer 8 · 2026-04-11 10:00:29

46

Views

How prove this floor function indentity

Published on 11 Apr 2026 - 10:00

score 425 · Answer 9 · 2026-04-14 20:06:03

425

Views

Prob. 10, Sec. 3.5, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: If $x_1 < x_2$ are arbitrary real numbers and . . .

Published on 14 Apr 2026 - 20:06

score 60 · Answer 10 · 2026-04-12 22:40:27

60

Views

Isolating $a_n$ in a recursive formula

Published on 12 Apr 2026 - 22:40

score 137 · Answer 11 · 2026-04-13 12:15:49

137

Views

Changing index sum of series

Published on 13 Apr 2026 - 12:15

score 244 · Answer 12 · 2026-04-17 12:57:05

244

Views

Is it true that if $\lim_{n\to\infty} n^\alpha a_n=+\infty$ for some $0<\alpha<1$ then $n(1-a_n/a_{n+1})\ge-\alpha$?

Published on 17 Apr 2026 - 12:57

score 134 · Answer 13 · 2026-03-25 01:18:34

134

Views

Is $\lim_{x\to \infty}{\sum_{i,h=1}^x \frac{1}{i^h} - x-\ln{x}}$ equal to $\gamma$, the Euler-Mascheroni constant? If so, why?

Published on 25 Mar 2026 - 1:18

score 78 · Answer 14 · 2026-04-15 20:02:51

78

Views

Cauchy sequence $a_{n}$ that has finitely many different values

Published on 15 Apr 2026 - 20:02

score 133 · Answer 15 · 2026-04-17 15:08:24

133

Views

$||f||=\max\limits_{0 \leq x \leq 1}|x^2f(x)|< \infty$ is not complete?

Published on 17 Apr 2026 - 15:08

List Question

Proving the existence of Pi with Derivatives and Sequences Only

Uniform convergence of trigonometric integral

Convergence of $\lim\limits_{n\to\infty}\frac{1}{n}\int_\limits{-n}^{n}\frac{1-e^{-nx^2}}{x^2(1+nx^2)}dx$

Explicit form of a double indexed sequence

Positive subsequence of a double sequence

About digamma function, does $\psi(a) =-\sum_{n=0}^{\infty} \frac{1} {n+a} ?$

Compute $\lim_{n\to\infty}\int_\limits{0}^{\infty}\frac{dx}{x^{n}+1}$

How prove this floor function indentity

Prob. 10, Sec. 3.5, in Bartle & Sherbert's INTRO TO REAL ANALYSIS: If $x_1 < x_2$ are arbitrary real numbers and . . .

Isolating $a_n$ in a recursive formula

Changing index sum of series

Is it true that if $\lim_{n\to\infty} n^\alpha a_n=+\infty$ for some $0<\alpha<1$ then $n(1-a_n/a_{n+1})\ge-\alpha$?

Is $\lim_{x\to \infty}{\sum_{i,h=1}^x \frac{1}{i^h} - x-\ln{x}}$ equal to $\gamma$, the Euler-Mascheroni constant? If so, why?

Cauchy sequence $a_{n}$ that has finitely many different values

$||f||=\max\limits_{0 \leq x \leq 1}|x^2f(x)|< \infty$ is not complete?

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