Question

Show that $\sum_{k=0}^n \frac{(2n)!}{{k!^2(n-k)!}^2}= \binom{2n}{n}^2$

score 141 · Answer 1 · 2026-04-16 00:10:14

141

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Show that $\sum_{k=0}^n \frac{(2n)!}{{k!^2(n-k)!}^2}= \binom{2n}{n}^2$

Published on 16 Apr 2026 - 0:10

score 373 · Answer 2 · 2026-04-14 19:33:14

373

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Finding the sum of $\cos45°$ + $i\cos135°$ + ... + $i^{n}\cos(45+90n)°$ + ... + $i^{40}\cos3645°$

Published on 14 Apr 2026 - 19:33

score 60 · Answer 3 · 2026-04-14 18:46:28

60

Views

Show that $\sum (-1)^n x^{(2^n)}$ has no limit as $x \uparrow 1$

Published on 14 Apr 2026 - 18:46

score 59 · Answer 4 · 2026-04-09 11:57:30

59

Views

Is it possible to put series in other series?

Published on 09 Apr 2026 - 11:57

score 1.2k · Answer 5 · 2026-04-14 17:17:18

1.2k

Views

Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion

Published on 14 Apr 2026 - 17:17

score 450 · Answer 6 · 2026-05-01 07:03:39

450

Views

How many egyptian fractions including and above (1/n) are necessary to sum to unity

Published on 01 May 2026 - 7:03

score 214 · Answer 7 · 2026-04-15 02:45:08

214

Views

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

Published on 15 Apr 2026 - 2:45

score 306 · Answer 8 · 2026-04-13 02:06:17

306

Views

Summation of $\sum_{n=0}^\infty e^{-\sqrt n}$

Published on 13 Apr 2026 - 2:06

score 57 · Answer 9 · 2026-03-26 01:14:34

57

Views

Natural Boundary of Sum $\sum_{n=0}^{\infty} e^{-b n^p}$

Published on 26 Mar 2026 - 1:14

score 122 · Answer 10 · 2026-04-10 20:05:16

122

Views

Difficult looking summation problem

Published on 10 Apr 2026 - 20:05

score 121 · Answer 11 · 2026-04-11 02:52:52

121

Views

Asymptotic Growth of Function of Prime Counting Function

Published on 11 Apr 2026 - 2:52

score 1.7k · Answer 12 · 2026-04-10 05:51:08

1.7k

Views

The sum of more than two consecutive natural numbers cannot be prime.

Published on 10 Apr 2026 - 5:51

score 172 · Answer 13 · 2026-04-14 03:24:16

172

Views

Multivariate sum over a simplex

Published on 14 Apr 2026 - 3:24

score 76 · Answer 14 · 2026-04-10 07:42:25

76

Views

How to I solve this summation?

Published on 10 Apr 2026 - 7:42

score 298 · Answer 15 · 2026-04-15 18:05:09

298

Views

Assuming $\sum_{n = 1}^\infty \int |f_n| < \infty$, properties that follow for integral

Published on 15 Apr 2026 - 18:05

List Question

Show that $\sum_{k=0}^n \frac{(2n)!}{{k!^2(n-k)!}^2}= \binom{2n}{n}^2$

Finding the sum of $\cos45°$ + $i\cos135°$ + ... + $i^{n}\cos(45+90n)°$ + ... + $i^{40}\cos3645°$

Show that $\sum (-1)^n x^{(2^n)}$ has no limit as $x \uparrow 1$

Is it possible to put series in other series?

Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion

How many egyptian fractions including and above (1/n) are necessary to sum to unity

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

Summation of $\sum_{n=0}^\infty e^{-\sqrt n}$

Natural Boundary of Sum $\sum_{n=0}^{\infty} e^{-b n^p}$

Difficult looking summation problem

Asymptotic Growth of Function of Prime Counting Function

The sum of more than two consecutive natural numbers cannot be prime.

Multivariate sum over a simplex

How to I solve this summation?

Assuming $\sum_{n = 1}^\infty \int |f_n| < \infty$, properties that follow for integral

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