Question

How to prove that $\sum_{i=1}^{m} 2^{i} B_{i}\binom{m}{i} \frac{1}{m-i+1}=\frac{2 m+1}{m+1}$ when $m$ is an even positive integer?

score 86 · Answer 1 · 2026-04-09 10:25:15

86

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How to prove that $\sum_{i=1}^{m} 2^{i} B_{i}\binom{m}{i} \frac{1}{m-i+1}=\frac{2 m+1}{m+1}$ when $m$ is an even positive integer?

Published on 09 Apr 2026 - 10:25

score 196 · Answer 2 · 2026-04-12 18:36:27

196

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PNT can't be applied Legendre's Conjecture as it can be to Bertrand's Postulate?

Published on 12 Apr 2026 - 18:36

score 166 · Answer 3 · 2026-04-12 01:36:58

166

Views

Prime counting function as ratio of polynomials.

Published on 12 Apr 2026 - 1:36

score 60 · Answer 4 · 2026-04-14 17:10:07

60

Views

Can Dirichlet characters mod q only agree on the same congruence class?

Published on 14 Apr 2026 - 17:10

score 99 · Answer 5 · 2026-04-15 18:28:40

99

Views

Do primes of the form $n^2+1$, proportional to $p_n^2$, converge?

Published on 15 Apr 2026 - 18:28

score 109 · Answer 6 · 2026-04-13 04:00:18

109

Views

About stronger version of Goldbach conjecture

Published on 13 Apr 2026 - 4:00

score 155 · Answer 7 · 2026-04-16 09:18:10

155

Views

Convergence of the double series $\sum_{d|n} \mu(d) x_{n}$

Published on 16 Apr 2026 - 9:18

score 122 · Answer 8 · 2026-04-11 17:48:13

122

Views

Find the residue of ζ(2s) and ζ(6s)

Published on 11 Apr 2026 - 17:48

score 29 · Answer 9 · 2026-04-15 08:11:15

Show that $F(s) = \log \zeta(s) + G(s)$ holds for $\text{Re }s>1$ and $F(s)$ does not have a meromorphic continuation for $\text{Re }s<1$.

score 86 · Answer 10 · 2026-04-16 09:04:08

86

Views

Help proving $\left|e^{-(s-1/2)\log(s)}e^s\right|\ll_\varepsilon e^{|s|^{1+\varepsilon}}$

Published on 16 Apr 2026 - 9:04

score 120 · Answer 11 · 2026-04-16 00:15:24

120

Views

How to show $\frac{\sigma(m!)}{m!}>ln(m)$?

Published on 16 Apr 2026 - 0:15

score 75 · Answer 12 · 2026-04-13 20:56:19

75

Views

The attractiveness of the fixed points in system $z \mapsto z + \xi(\frac{1}{2} + i z)$

Published on 13 Apr 2026 - 20:56

score 65 · Answer 13 · 2026-04-09 14:47:38

65

Views

Want to show $\sum_{n>N}n^{-1/2} \ll N^{-1/2}$

Published on 09 Apr 2026 - 14:47

score 3.1k · Answer 14 · 2026-04-13 08:39:06

3.1k

Views

Why is proving the Riemann Hypothesis so hard?

Published on 13 Apr 2026 - 8:39

score 76 · Answer 15 · 2026-04-14 12:06:26

76

Views

Asymptotic relation of $\sum_{n > x}\frac{1}{n^2}$

Published on 14 Apr 2026 - 12:06

List Question

How to prove that $\sum_{i=1}^{m} 2^{i} B_{i}\binom{m}{i} \frac{1}{m-i+1}=\frac{2 m+1}{m+1}$ when $m$ is an even positive integer?

PNT can't be applied Legendre's Conjecture as it can be to Bertrand's Postulate?

Prime counting function as ratio of polynomials.

Can Dirichlet characters mod q only agree on the same congruence class?

Do primes of the form $n^2+1$, proportional to $p_n^2$, converge?

About stronger version of Goldbach conjecture

Convergence of the double series $\sum_{d|n} \mu(d) x_{n}$

Find the residue of ζ(2s) and ζ(6s)

Show that $F(s) = \log \zeta(s) + G(s)$ holds for $\text{Re }s>1$ and $F(s)$ does not have a meromorphic continuation for $\text{Re }s<1$.

Help proving $\left|e^{-(s-1/2)\log(s)}e^s\right|\ll_\varepsilon e^{|s|^{1+\varepsilon}}$

How to show $\frac{\sigma(m!)}{m!}>ln(m)$?

The attractiveness of the fixed points in system $z \mapsto z + \xi(\frac{1}{2} + i z)$

Want to show $\sum_{n>N}n^{-1/2} \ll N^{-1/2}$

Why is proving the Riemann Hypothesis so hard?

Asymptotic relation of $\sum_{n > x}\frac{1}{n^2}$

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