Question

Is there any proof of cauchy formula for repeated integration without induction?

score 108 · Answer 1 · 2018-08-08 17:52:19

108

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Is there any proof of cauchy formula for repeated integration without induction?

Published on 08 Aug 2018 - 17:52

score 266 · Answer 2 · 2026-03-25 11:22:18

266

Views

Application of Implicit Function Theorem: Problem 2-40 from Spivak's Calculus on Manifolds

Published on 25 Mar 2026 - 11:22

score 311 · Answer 3 · 2026-03-25 07:46:27

311

Views

Can we prove that $\lim_{n\to\infty} \frac{1^{n_0}+2^{n_0}+\cdots+n^{n_0}}{n^{n_0+1}}$ is finite for any $n_0\in\Bbb N$ without a direct computation?

Published on 25 Mar 2026 - 7:46

score 89 · Answer 4 · 2026-03-26 09:40:23

89

Views

Riemann Integrability of a function $f$ on $[0,1]$

Published on 26 Mar 2026 - 9:40

score 508 · Answer 5 · 2018-08-15 07:37:46

508

Views

Convergence of a logarithmic sequence

Published on 15 Aug 2018 - 7:37

score 122 · Answer 6 · 2018-08-20 13:29:15

122

Views

Proof explanation: Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$

Published on 20 Aug 2018 - 13:29

score 1.2k · Answer 7 · 2026-03-25 19:03:47

1.2k

Views

Proof about a theorem that says a function is continuous if only if f is right continuous in a and left continuous.

Published on 25 Mar 2026 - 19:03

score 71 · Answer 8 · 2026-03-25 19:11:22

71

Views

Questions on the length of a positive integer $a\in \mathbb{Z}^+$.

Published on 25 Mar 2026 - 19:11

score 270 · Answer 9 · 2018-08-27 07:25:01

270

Views

Prove cyclic subgroup has n distinct elements $\langle x \rangle = \{1,x,x^2,..,x^{n-1}\}$ without using Euclidean algorithm again

Published on 27 Aug 2018 - 7:25

score 486 · Answer 10 · 2018-08-27 23:30:51

486

Views

Prove that $1+x<e^x$ for all real numbers $x\neq0$.

Published on 27 Aug 2018 - 23:30

score 31 · Answer 11 · 2026-03-25 09:38:50

31

Views

Proof of a practical method of a natural number's equation

Published on 25 Mar 2026 - 9:38

score 1k · Answer 12 · 2018-08-28 19:19:43

1k

Views

Alternative proof of Levy's continuity theorem(problem with understanding specific part)

Published on 28 Aug 2018 - 19:19

score 64 · Answer 13 · 2026-03-25 04:40:40

64

Views

Determining whether proofs of the Pythagorean theorem are essentially the same, or essentially different

Published on 25 Mar 2026 - 4:40

score 187 · Answer 14 · 2026-03-25 16:46:29

187

Views

How would Euclid have proved that $ a \times b = ((ab)/c) \times c$?

Published on 25 Mar 2026 - 16:46

score 253 · Answer 15 · 2018-08-30 03:13:55

253

Views

Proof verification $(x_1^2 + x_2^2)(y_1^2 + y_2^2) = (x_1y_1 + x_2y_2)^2+ (x_1y_2 - x_2y_1)^2$ (Spivak's Calculus)

Published on 30 Aug 2018 - 3:13

List Question

Is there any proof of cauchy formula for repeated integration without induction?

Application of Implicit Function Theorem: Problem 2-40 from Spivak's Calculus on Manifolds

Can we prove that $\lim_{n\to\infty} \frac{1^{n_0}+2^{n_0}+\cdots+n^{n_0}}{n^{n_0+1}}$ is finite for any $n_0\in\Bbb N$ without a direct computation?

Riemann Integrability of a function $f$ on $[0,1]$

Convergence of a logarithmic sequence

Proof explanation: Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$

Proof about a theorem that says a function is continuous if only if f is right continuous in a and left continuous.

Questions on the length of a positive integer $a\in \mathbb{Z}^+$.

Prove cyclic subgroup has n distinct elements $\langle x \rangle = \{1,x,x^2,..,x^{n-1}\}$ without using Euclidean algorithm again

Prove that $1+x<e^x$ for all real numbers $x\neq0$.

Proof of a practical method of a natural number's equation

Alternative proof of Levy's continuity theorem(problem with understanding specific part)

Determining whether proofs of the Pythagorean theorem are essentially the same, or essentially different

How would Euclid have proved that $ a \times b = ((ab)/c) \times c$?

Proof verification $(x_1^2 + x_2^2)(y_1^2 + y_2^2) = (x_1y_1 + x_2y_2)^2+ (x_1y_2 - x_2y_1)^2$ (Spivak's Calculus)

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