Question

Solutions of $\ f(x) = \frac{1}{x-a_1} + \frac{1}{x-a_2} + \cdots + \frac{1}{x-a_n} $

score 87 · Answer 1 · 2026-04-16 14:13:41

87

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Solutions of $\ f(x) = \frac{1}{x-a_1} + \frac{1}{x-a_2} + \cdots + \frac{1}{x-a_n} $

Published on 16 Apr 2026 - 14:13

score 101 · Answer 2 · 2026-04-17 06:27:47

101

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Show that: $\sum_{l=0}^{m}(-1)^{m+l}4^{l-1}l{m \choose l}{2l \choose l}^{-1}{m+l \choose l}=\sum_{i=1}^{m}i^2$

Published on 17 Apr 2026 - 6:27

score 44 · Answer 3 · 2026-04-14 03:39:02

44

Views

If a sum of positive terms is O(n^2), then the terms are O(n)?

Published on 14 Apr 2026 - 3:39

score 40 · Answer 4 · 2026-04-15 13:32:47

40

Views

Calculating the summation $\sum_{n=0}^{\infty} \frac{n^3}{3^n}$

Published on 15 Apr 2026 - 13:32

score 51 · Answer 5 · 2026-04-11 12:16:41

51

Views

How do I get variable x inside this summation formula?

Published on 11 Apr 2026 - 12:16

score 45 · Answer 6 · 2026-04-11 02:55:12

45

Views

iterate sum with powers

Published on 11 Apr 2026 - 2:55

score 189 · Answer 7 · 2026-04-12 09:54:42

189

Views

Egyptian fractions with prime power denominators summing to 1?

Published on 12 Apr 2026 - 9:54

score 21 · Answer 8 · 2026-04-14 07:37:28

21

Views

Summation Formula as an answer:

Published on 14 Apr 2026 - 7:37

score 73 · Answer 9 · 2026-04-15 20:33:57

73

Views

Compute: $\lim_{n\to\infty}\sum_{i=1}^{2n^4+n^2}\frac{5n^2+1}{n^4+i}$

Published on 15 Apr 2026 - 20:33

score 57 · Answer 10 · 2026-03-25 09:31:33

57

Views

What does this double summation with mod evaluate to?

Published on 25 Mar 2026 - 9:31

score 111 · Answer 11 · 2026-04-16 10:04:33

111

Views

Calculating the sum $\sum_{n=1}^{\infty} \left(\dfrac{2}{n}\right)^n$

Published on 16 Apr 2026 - 10:04

score 68 · Answer 12 · 2026-04-13 14:48:31

68

Views

Prove that these two series are equal

Published on 13 Apr 2026 - 14:48

score 237 · Answer 13 · 2026-04-13 11:37:04

237

Views

Finite sums involving Stirling number of first kind

Published on 13 Apr 2026 - 11:37

score 34 · Answer 14 · 2026-04-16 15:08:23

34

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Prove that $\sum_{k=0}^{ \frac{n^2}{2}} 2^{n^2-2k}\binom{n^2}{2k} = \frac{3^{n^2}+1}{2}$

Published on 16 Apr 2026 - 15:08

score 102 · Answer 15 · 2026-04-13 23:02:03

102

Views

How to show that $\sum_{n=0}^{N}\frac{(-1)^n}{{(N+n)!}(N-n)!}=\frac{1}{2N!^2}$?

Published on 13 Apr 2026 - 23:02

List Question

Solutions of $\ f(x) = \frac{1}{x-a_1} + \frac{1}{x-a_2} + \cdots + \frac{1}{x-a_n} $

Show that: $\sum_{l=0}^{m}(-1)^{m+l}4^{l-1}l{m \choose l}{2l \choose l}^{-1}{m+l \choose l}=\sum_{i=1}^{m}i^2$

If a sum of positive terms is O(n^2), then the terms are O(n)?

Calculating the summation $\sum_{n=0}^{\infty} \frac{n^3}{3^n}$

How do I get variable x inside this summation formula?

iterate sum with powers

Egyptian fractions with prime power denominators summing to 1?

Summation Formula as an answer:

Compute: $\lim_{n\to\infty}\sum_{i=1}^{2n^4+n^2}\frac{5n^2+1}{n^4+i}$

What does this double summation with mod evaluate to?

Calculating the sum $\sum_{n=1}^{\infty} \left(\dfrac{2}{n}\right)^n$

Prove that these two series are equal

Finite sums involving Stirling number of first kind

Prove that $\sum_{k=0}^{ \frac{n^2}{2}} 2^{n^2-2k}\binom{n^2}{2k} = \frac{3^{n^2}+1}{2}$

How to show that $\sum_{n=0}^{N}\frac{(-1)^n}{{(N+n)!}(N-n)!}=\frac{1}{2N!^2}$?

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