Question

Closed form of $\sum_{k=1}^{n} \frac{{n}\choose{k}}{k}$.

score 138 · Answer 1 · 2026-03-25 11:14:47

138

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Closed form of $\sum_{k=1}^{n} \frac{{n}\choose{k}}{k}$.

Published on 25 Mar 2026 - 11:14

score 166 · Answer 2 · 2026-04-14 13:31:56

166

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Proof for the general formula for $a^n+b^n$.

Published on 14 Apr 2026 - 13:31

score 53 · Answer 3 · 2026-04-10 13:35:13

53

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How to compute a simple sum

Published on 10 Apr 2026 - 13:35

score 66 · Answer 4 · 2026-04-15 07:59:31

66

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Let $f$ be a continuous function on $\mathbb{R}$ satisfying $\int_\mathbb{R}|f(x)|dx<\infty$. Can we conclude that $\sum_\mathbb{Z}|f(k)|<\infty$?

Published on 15 Apr 2026 - 7:59

score 42 · Answer 5 · 2026-04-16 18:18:29

42

Views

What's the proof for this summation with dependent variables?

Published on 16 Apr 2026 - 18:18

score 111 · Answer 6 · 2026-04-17 01:01:54

111

Views

If $ 1+ \frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}=\frac{A}{B}$ where $A$ and $B$ are coprime positive integers, then $5\nmid A$ and $5\nmid B$.

Published on 17 Apr 2026 - 1:01

score 80 · Answer 7 · 2026-04-13 01:54:37

80

Views

Sum of reciprocals of odd prime numbers equal to one

Published on 13 Apr 2026 - 1:54

score 201 · Answer 8 · 2026-04-15 20:30:13

201

Views

For $a,b,c>0$ prove that $abc(a+b+c) \le a^3 b + b^3 c + c^3 a$

Published on 15 Apr 2026 - 20:30

score 28 · Answer 9 · 2026-04-12 10:37:20

28

Views

Proving a series is less than an expression

Published on 12 Apr 2026 - 10:37

score 50 · Answer 10 · 2026-04-11 16:16:40

50

Views

Calculate a finite sum

Published on 11 Apr 2026 - 16:16

score 108 · Answer 11 · 2026-05-14 10:07:09

108

Views

Help understanding $1+2+3+\dots+n$, proof

Published on 14 May 2026 - 10:07

score 45 · Answer 12 · 2026-04-11 19:47:34

45

Views

Sum with unit steps

Published on 11 Apr 2026 - 19:47

score 287 · Answer 13 · 2026-04-14 02:06:26

287

Views

How to prove that $\sum_{k=0}^n{(-1)^k{4n-2k\choose 2n}{2n\choose k}}=2^{2n}$?

Published on 14 Apr 2026 - 2:06

score 156 · Answer 14 · 2026-04-11 06:06:50

156

Views

What's the general formula for the sum total of first k terms of the following?

Published on 11 Apr 2026 - 6:06

score 23 · Answer 15 · 2026-04-13 17:37:51

23

Views

Recursive formula $\pi_i = 2 \rho^i \pi_0$ with $\sum^4_{i=0} \pi_i =1$ yields $\pi_0 = \frac{1-\rho}{1+\rho-2\rho^5}$?

Published on 13 Apr 2026 - 17:37

List Question

Closed form of $\sum_{k=1}^{n} \frac{{n}\choose{k}}{k}$.

Proof for the general formula for $a^n+b^n$.

How to compute a simple sum

Let $f$ be a continuous function on $\mathbb{R}$ satisfying $\int_\mathbb{R}|f(x)|dx<\infty$. Can we conclude that $\sum_\mathbb{Z}|f(k)|<\infty$?

What's the proof for this summation with dependent variables?

If $ 1+ \frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}=\frac{A}{B}$ where $A$ and $B$ are coprime positive integers, then $5\nmid A$ and $5\nmid B$.

Sum of reciprocals of odd prime numbers equal to one

For $a,b,c>0$ prove that $abc(a+b+c) \le a^3 b + b^3 c + c^3 a$

Proving a series is less than an expression

Calculate a finite sum

Help understanding $1+2+3+\dots+n$, proof

Sum with unit steps

How to prove that $\sum_{k=0}^n{(-1)^k{4n-2k\choose 2n}{2n\choose k}}=2^{2n}$?

What's the general formula for the sum total of first k terms of the following?

Recursive formula $\pi_i = 2 \rho^i \pi_0$ with $\sum^4_{i=0} \pi_i =1$ yields $\pi_0 = \frac{1-\rho}{1+\rho-2\rho^5}$?

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