Question

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

score 111 · Answer 1 · 2026-04-09 20:03:16

111

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

Published on 09 Apr 2026 - 20:03

score 267 · Answer 2 · 2026-05-10 19:03:14

267

Views

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

Published on 10 May 2026 - 19:03

score 314 · Answer 3 · 2026-05-10 21:37:10

314

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 10 May 2026 - 21:37

score 91 · Answer 4 · 2026-04-11 18:10:28

91

Views

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

Published on 11 Apr 2026 - 18:10

score 511 · Answer 5 · 2026-04-13 19:33:17

511

Views

Convergence of a logarithmic sequence

Published on 13 Apr 2026 - 19:33

score 125 · Answer 6 · 2026-04-15 09:18:34

125

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 15 Apr 2026 - 9:18

score 1.2k · Answer 7 · 2026-04-11 02:27:56

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 11 Apr 2026 - 2:27

score 74 · Answer 8 · 2026-05-11 05:28:48

74

Views

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

Published on 11 May 2026 - 5:28

score 273 · Answer 9 · 2026-04-15 22:27:38

273

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 15 Apr 2026 - 22:27

score 489 · Answer 10 · 2026-04-16 03:36:43

489

Views

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

Published on 16 Apr 2026 - 3:36

score 34 · Answer 11 · 2026-05-11 01:48:42

34

Views

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

Published on 11 May 2026 - 1:48

score 1k · Answer 12 · 2026-04-09 06:23:34

1k

Views

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

Published on 09 Apr 2026 - 6:23

score 67 · Answer 13 · 2026-05-11 05:27:57

67

Views

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

Published on 11 May 2026 - 5:27

score 189 · Answer 14 · 2026-04-15 07:18:56

189

Views

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

Published on 15 Apr 2026 - 7:18

score 256 · Answer 15 · 2026-04-17 06:12:11

256

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 17 Apr 2026 - 6:12

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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