Question

Finding $\frac{d^{n-1}}{dx^{n-1}}(1+\sqrt x)^{2n}|_{x=1}$

score 61 · Answer 1 · 2018-12-10 08:31:59

61

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Finding $\frac{d^{n-1}}{dx^{n-1}}(1+\sqrt x)^{2n}|_{x=1}$

Published on 10 Dec 2018 - 8:31

score 101 · Answer 2 · 2026-03-26 22:17:40

101

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Simpler ways to show that $n^2$ divides a polynomial?

Published on 26 Mar 2026 - 22:17

score 216 · Answer 3 · 2018-12-12 11:27:28

216

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Collecting proofs for $\sum_{n=2}^{\infty} \, \frac{n-1}{2^n} = 1$

Published on 12 Dec 2018 - 11:27

score 89 · Answer 4 · 2018-12-12 15:15:38

89

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Conditions for a modular multiplication graph to contain $k$-cycles

Published on 12 Dec 2018 - 15:15

score 98 · Answer 5 · 2018-12-14 03:33:25

98

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Suppose $\lim_{n \to \infty}a_n=a$, Prove $\lim_{n\to \infty} \frac{1}{2^n} \sum_{k=0}^n \binom{n}{k}a_k=a$.

Published on 14 Dec 2018 - 3:33

score 514 · Answer 6 · 2026-03-25 03:04:15

514

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If $f : M \to N$ is $C^k$, then $\Gamma(f)$ is a closed embedded submanifold of $M \times N$

Published on 25 Mar 2026 - 3:04

score 346 · Answer 7 · 2026-03-25 05:05:41

346

Views

Newtonian potential expansion identity

Published on 25 Mar 2026 - 5:05

score 151 · Answer 8 · 2026-03-25 04:59:49

151

Views

Proof verification: For $a$, $b$, $c$ positive with $abc=1$, show $\sum_{\text{cyc}}\frac{1}{a^3(b+c)}\geq \frac32$

Published on 25 Mar 2026 - 4:59

score 174 · Answer 9 · 2018-12-19 07:09:33

174

Views

Is there a proof of the real form of Fourier's Theorem?

Published on 19 Dec 2018 - 7:09

score 91 · Answer 10 · 2018-12-19 12:09:49

91

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Proving that any given element $hk$ appears $|H \cap K|$ times as a product in the list of $HK$

Published on 19 Dec 2018 - 12:09

score 199 · Answer 11 · 2018-12-20 11:30:56

199

Views

Is there an elementary proof of Fourier's Theorem?

Published on 20 Dec 2018 - 11:30

score 502 · Answer 12 · 2026-03-25 01:21:17

502

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Prove constructively that $\log_2 3$ is irrational.

Published on 25 Mar 2026 - 1:21

score 64 · Answer 13 · 2026-03-25 17:33:21

64

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Proving mean of sample minimum of U[0,1] is 1/(n+1) without calculus

Published on 25 Mar 2026 - 17:33

score 327 · Answer 14 · 2018-12-24 04:52:59

327

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Let $\left\{ H_i | i \in I\right\}$ be a family of subgroups of G. State and prove a condition which makes $\cup_{i \in I} H_{i}$ a subgroup of $G$

Published on 24 Dec 2018 - 4:52

score 544 · Answer 15 · 2018-12-24 12:46:43

544

Views

Show that $\sum\limits_{n\ge1}\frac1{n^2}=\sum\limits_{n\ge1}\frac3{n^2\binom{2n}n}$ without actually evaluating both series

Published on 24 Dec 2018 - 12:46

List Question

Finding $\frac{d^{n-1}}{dx^{n-1}}(1+\sqrt x)^{2n}|_{x=1}$

Simpler ways to show that $n^2$ divides a polynomial?

Collecting proofs for $\sum_{n=2}^{\infty} \, \frac{n-1}{2^n} = 1$

Conditions for a modular multiplication graph to contain $k$-cycles

Suppose $\lim_{n \to \infty}a_n=a$, Prove $\lim_{n\to \infty} \frac{1}{2^n} \sum_{k=0}^n \binom{n}{k}a_k=a$.

If $f : M \to N$ is $C^k$, then $\Gamma(f)$ is a closed embedded submanifold of $M \times N$

Newtonian potential expansion identity

Proof verification: For $a$, $b$, $c$ positive with $abc=1$, show $\sum_{\text{cyc}}\frac{1}{a^3(b+c)}\geq \frac32$

Is there a proof of the real form of Fourier's Theorem?

Proving that any given element $hk$ appears $|H \cap K|$ times as a product in the list of $HK$

Is there an elementary proof of Fourier's Theorem?

Prove constructively that $\log_2 3$ is irrational.

Proving mean of sample minimum of U[0,1] is 1/(n+1) without calculus

Let $\left\{ H_i | i \in I\right\}$ be a family of subgroups of G. State and prove a condition which makes $\cup_{i \in I} H_{i}$ a subgroup of $G$

Show that $\sum\limits_{n\ge1}\frac1{n^2}=\sum\limits_{n\ge1}\frac3{n^2\binom{2n}n}$ without actually evaluating both series

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