Question

Calculating $1-\frac{1}{2^4}+\frac{1}{3^4}-\frac{1}{4^4} \ldots$ using Fourier series

score 66 · Answer 1 · 2026-04-16 18:03:52

66

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Calculating $1-\frac{1}{2^4}+\frac{1}{3^4}-\frac{1}{4^4} \ldots$ using Fourier series

Published on 16 Apr 2026 - 18:03

score 540 · Answer 2 · 2026-04-16 01:31:52

540

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what is result $T(n)=\sum_{i=1}^n T(i-1) T(n-i)$

Published on 16 Apr 2026 - 1:31

score 83 · Answer 3 · 2026-04-14 04:16:38

83

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How to prove $\sum\limits_{k=0}^{N} \frac{(-1)^k {N \choose k}}{(k+1)^2} = \frac{1}{N+1} \sum\limits_{n=1}^{N+1} \frac{1}{n}$

Published on 14 Apr 2026 - 4:16

score 29 · Answer 4 · 2026-04-12 04:07:21

29

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Confusing Coefficients in infinite sum

Published on 12 Apr 2026 - 4:07

score 38 · Answer 5 · 2026-04-16 09:01:56

38

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Differentiability and Taylor series of $\sum_{k=0}^{\infty} \frac{1}{k ! \cdot\left(1+4^{k} x^{2}\right)}$.

Published on 16 Apr 2026 - 9:01

score 46 · Answer 6 · 2026-04-25 17:24:30

46

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Extracting term from sum with index changes, where do I is misunderstood the solution?

Published on 25 Apr 2026 - 17:24

score 59 · Answer 7 · 2026-04-12 16:23:15

59

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How do you eliminate this constant from this summation?

Published on 12 Apr 2026 - 16:23

score 91 · Answer 8 · 2026-04-16 12:51:18

91

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How to prove $n \ge 2 {\left ( \sum_{k=1}^n \frac{1}{k} \right)}^2$ for all $n \ge 2$?

Published on 16 Apr 2026 - 12:51

score 76 · Answer 9 · 2026-03-25 11:04:31

76

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Prove that $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ $\geq$ $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$

Published on 25 Mar 2026 - 11:04

score 73 · Answer 10 · 2026-04-15 12:31:18

73

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Is there a closed formula for the sum $q+q^2+q^4+\dots+q^{2^n}$?

Published on 15 Apr 2026 - 12:31

score 38 · Answer 11 · 2026-04-16 00:16:38

38

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Simplifying $R_1R_2R_3 + R_1R_2R_4 + R_1R_3R_4 + R_2R_3R_4$ pattern

Published on 16 Apr 2026 - 0:16

score 60 · Answer 12 · 2026-04-14 09:30:53

60

Views

Prove the following summation identity

Published on 14 Apr 2026 - 9:30

score 240 · Answer 13 · 2026-04-09 13:54:55

240

Views

Evaluating the expression: $\sum\limits_1^n(-1)^{k-1}\frac{n \choose k}{k^2}$

Published on 09 Apr 2026 - 13:54

score 108 · Answer 14 · 2026-04-21 06:12:57

108

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Sum of the given series: $(1^2 - 1 + 1)(1!) + (2^2 - 2 + 1)(2!) + \cdots + (n^2 - n + 1)(n!) $

Published on 21 Apr 2026 - 6:12

score 108 · Answer 15 · 2026-03-26 14:34:46

108

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Show that for $r,n \in \mathbb{N}$ with $r \geq n$, $\sum_{i=0}^{n-1} (-1)^i \binom{n}{i} \binom{r+n-i-1}{r} = \binom{r-1}{n-1}$

Published on 26 Mar 2026 - 14:34

List Question

Calculating $1-\frac{1}{2^4}+\frac{1}{3^4}-\frac{1}{4^4} \ldots$ using Fourier series

what is result $T(n)=\sum_{i=1}^n T(i-1) T(n-i)$

How to prove $\sum\limits_{k=0}^{N} \frac{(-1)^k {N \choose k}}{(k+1)^2} = \frac{1}{N+1} \sum\limits_{n=1}^{N+1} \frac{1}{n}$

Confusing Coefficients in infinite sum

Differentiability and Taylor series of $\sum_{k=0}^{\infty} \frac{1}{k ! \cdot\left(1+4^{k} x^{2}\right)}$.

Extracting term from sum with index changes, where do I is misunderstood the solution?

How do you eliminate this constant from this summation?

How to prove $n \ge 2 {\left ( \sum_{k=1}^n \frac{1}{k} \right)}^2$ for all $n \ge 2$?

Prove that $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ $\geq$ $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$

Is there a closed formula for the sum $q+q^2+q^4+\dots+q^{2^n}$?

Simplifying $R_1R_2R_3 + R_1R_2R_4 + R_1R_3R_4 + R_2R_3R_4$ pattern

Prove the following summation identity

Evaluating the expression: $\sum\limits_1^n(-1)^{k-1}\frac{n \choose k}{k^2}$

Sum of the given series: $(1^2 - 1 + 1)(1!) + (2^2 - 2 + 1)(2!) + \cdots + (n^2 - n + 1)(n!) $

Show that for $r,n \in \mathbb{N}$ with $r \geq n$, $\sum_{i=0}^{n-1} (-1)^i \binom{n}{i} \binom{r+n-i-1}{r} = \binom{r-1}{n-1}$

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