Question

Alternative approaches to showing that $\Gamma'(1/2)=-\sqrt\pi\left(\gamma+\log(4)\right)$

score 578 · Answer 1 · 2026-03-25 14:26:05

578

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Alternative approaches to showing that $\Gamma'(1/2)=-\sqrt\pi\left(\gamma+\log(4)\right)$

Published on 25 Mar 2026 - 14:26

score 117 · Answer 2 · 2020-06-28 23:03:25

117

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easiest proof of the Prime Number Theorem to study and teach?

Published on 28 Jun 2020 - 23:03

score 221 · Answer 3 · 2020-06-29 07:08:59

221

Views

Can this inductive proof that $\sum_{i=0}^n2^{2i+1}=\frac23(4^n-1)$ be simplified?

Published on 29 Jun 2020 - 7:08

score 288 · Answer 4 · 2020-06-29 17:16:57

288

Views

Is this proof that $\sqrt 2 \in R$ correct?

Published on 29 Jun 2020 - 17:16

score 123 · Answer 5 · 2020-07-01 01:19:44

123

Views

Show that if $|z| < 1$, then $\displaystyle\frac{z}{1+z} + \frac{2z^{2}}{1+z^{2}} + \frac{4z^{4}}{1+z^{4}} + \frac{8z^{8}}{1+z^{8}} + \ldots$

Published on 01 Jul 2020 - 1:19

score 242 · Answer 6 · 2020-07-01 01:59:25

242

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Does the following series converge or diverge: $\sum_{n=1}^{\infty}\frac{n!}{n^{n}}$?

Published on 01 Jul 2020 - 1:59

score 70 · Answer 7 · 2026-03-27 00:01:40

70

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Is this proof valid?

Published on 27 Mar 2026 - 0:01

score 145 · Answer 8 · 2026-03-26 15:17:09

145

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Line $K$ is parallel to line $U$, and line $L$ intersects line $K$ at point $P$. Show $L \nparallel U$.

Published on 26 Mar 2026 - 15:17

score 74 · Answer 9 · 2020-07-02 20:24:12

74

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Let $a_{n} = \sqrt{n^{2}+n} - n$, for $n\in\textbf{N}$. Is the sequence $(a_{n})_{n=1}^{\infty}$ monotonic?

Published on 02 Jul 2020 - 20:24

score 77 · Answer 10 · 2020-07-02 22:36:20

77

Views

Show that $|z_1 + z_2|^2 + |z_1 - z_2|^2 = 2|z_1|^2 + 2|z_2|^2$. Find a corresponding result for a finite set $\{z_1,z_2,\ldots,z_n\}$.

Published on 02 Jul 2020 - 22:36

score 276 · Answer 11 · 2020-07-03 18:49:30

276

Views

Show that if $|z| < 1$ then the series $\sum_{n=0}^{\infty}(n+1)z^{n}$ converges, and find its sum.

Published on 03 Jul 2020 - 18:49

score 72 · Answer 12 · 2020-07-03 19:34:13

72

Views

Show that if $\sum_{n=1}^{\infty}a_{n}$ converges, then so do $\sum_{n=1}^{\infty}a^{2}_{n}$ and $\sum_{n=1}^{\infty}a_{n}/(1-a_{n})$.

Published on 03 Jul 2020 - 19:34

score 446 · Answer 13 · 2026-03-30 20:45:11

446

Views

Locus of the circumcenter of triangle formed by the axes and tangent to a given circle.

Published on 30 Mar 2026 - 20:45

score 68 · Answer 14 · 2026-03-26 15:16:56

68

Views

If $L_1$ is perpendicular to line $K$, and $L_2$ is also perpendicular to line $K$, then $L_1$ is parallel to $L_2$.

Published on 26 Mar 2026 - 15:16

score 74 · Answer 15 · 2020-07-05 19:38:38

74

Views

For all sets $A$ and $B$, ( $A \cap B = A \cup B \implies A = B$ )

Published on 05 Jul 2020 - 19:38

List Question

Alternative approaches to showing that $\Gamma'(1/2)=-\sqrt\pi\left(\gamma+\log(4)\right)$

easiest proof of the Prime Number Theorem to study and teach?

Can this inductive proof that $\sum_{i=0}^n2^{2i+1}=\frac23(4^n-1)$ be simplified?

Is this proof that $\sqrt 2 \in R$ correct?

Show that if $|z| < 1$, then $\displaystyle\frac{z}{1+z} + \frac{2z^{2}}{1+z^{2}} + \frac{4z^{4}}{1+z^{4}} + \frac{8z^{8}}{1+z^{8}} + \ldots$

Does the following series converge or diverge: $\sum_{n=1}^{\infty}\frac{n!}{n^{n}}$?

Is this proof valid?

Line $K$ is parallel to line $U$, and line $L$ intersects line $K$ at point $P$. Show $L \nparallel U$.

Let $a_{n} = \sqrt{n^{2}+n} - n$, for $n\in\textbf{N}$. Is the sequence $(a_{n})_{n=1}^{\infty}$ monotonic?

Show that $|z_1 + z_2|^2 + |z_1 - z_2|^2 = 2|z_1|^2 + 2|z_2|^2$. Find a corresponding result for a finite set $\{z_1,z_2,\ldots,z_n\}$.

Show that if $|z| < 1$ then the series $\sum_{n=0}^{\infty}(n+1)z^{n}$ converges, and find its sum.

Show that if $\sum_{n=1}^{\infty}a_{n}$ converges, then so do $\sum_{n=1}^{\infty}a^{2}_{n}$ and $\sum_{n=1}^{\infty}a_{n}/(1-a_{n})$.

Locus of the circumcenter of triangle formed by the axes and tangent to a given circle.

If $L_1$ is perpendicular to line $K$, and $L_2$ is also perpendicular to line $K$, then $L_1$ is parallel to $L_2$.

For all sets $A$ and $B$, ( $A \cap B = A \cup B \implies A = B$ )

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