Question

Limit $\lim\limits_{n \to \infty} \sum\limits_{k = 0}^n \dfrac{1}{qn+kp+1}$

score 241 · Answer 1 · 2026-04-13 04:30:26

241

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Limit $\lim\limits_{n \to \infty} \sum\limits_{k = 0}^n \dfrac{1}{qn+kp+1}$

Published on 13 Apr 2026 - 4:30

score 91 · Answer 2 · 2026-04-12 23:25:29

91

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Sum of products of binomial coefficients: $\sum\limits_{k=0}^{19}\binom{18}k\binom{20}k$

Published on 12 Apr 2026 - 23:25

score 232 · Answer 3 · 2026-03-25 06:09:19

232

Views

How to write combinations using double summation

Published on 25 Mar 2026 - 6:09

score 163 · Answer 4 · 2026-04-10 21:56:22

163

Views

sum involving Laguerre polynomial

Published on 10 Apr 2026 - 21:56

score 38 · Answer 5 · 2026-04-16 12:19:26

38

Views

Values of x of convergence and absolute convergence $\sum_{n=0}^{\infty} \frac{n!(2n)!}{(3n)!}x^n$

Published on 16 Apr 2026 - 12:19

score 671 · Answer 6 · 2026-04-17 08:12:59

671

Views

Rewriting a double summation.

Published on 17 Apr 2026 - 8:12

score 26 · Answer 7 · 2026-04-17 09:01:41

26

Views

Prove area using simple sums and given sum

Published on 17 Apr 2026 - 9:01

score 54 · Answer 8 · 2026-04-15 06:03:39

54

Views

Show that $\sum_{k=0}^\infty \frac{e^{-x}(k-x)^2x^k}{k!} = x$

Published on 15 Apr 2026 - 6:03

score 116 · Answer 9 · 2026-04-08 21:48:03

116

Views

Is it possible to express this sum in a closed form?

Published on 08 Apr 2026 - 21:48

score 83 · Answer 10 · 2026-04-23 11:06:44

83

Views

Summing discrete coordinate lengths, a generalized n-dimensional case

Published on 23 Apr 2026 - 11:06

score 1.2k · Answer 11 · 2026-04-12 20:41:51

1.2k

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How to evaluate $\sum\limits_{n=0}^\infty n^3x^n$, for $x\in[0,1)$.

Published on 12 Apr 2026 - 20:41

score 967 · Answer 12 · 2026-04-12 08:51:55

967

Views

Calculating Bernstein polynomial for function $x^3$.

Published on 12 Apr 2026 - 8:51

score 88 · Answer 13 · 2026-04-16 07:24:56

88

Views

find a closed form expression for $\sum_{k=0}^n \left \lceil\sqrt{2k} \right\rceil, \quad n \ge 0$

Published on 16 Apr 2026 - 7:24

score 176 · Answer 14 · 2026-03-25 11:04:50

176

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$x,y,z>0$, prove:$\frac{x}{y+z+\sqrt[4]\frac{y^4+z^4}{2}}+\frac{y}{z+x+\sqrt[4]\frac{z^4+x^4}{2}}+\frac{z}{x+y+\sqrt[4]\frac{x^4+y^4}{2}}\geq1$

Published on 25 Mar 2026 - 11:04

score 75 · Answer 15 · 2026-04-16 02:10:19

75

Views

Does $\lim_{x \to 1^{-}} \sum_{n=0}^{\infty} (x^n - x^{n+1})\log{(1+x^{n+1})} = 0$?

Published on 16 Apr 2026 - 2:10

List Question

Limit $\lim\limits_{n \to \infty} \sum\limits_{k = 0}^n \dfrac{1}{qn+kp+1}$

Sum of products of binomial coefficients: $\sum\limits_{k=0}^{19}\binom{18}k\binom{20}k$

How to write combinations using double summation

sum involving Laguerre polynomial

Values of x of convergence and absolute convergence $\sum_{n=0}^{\infty} \frac{n!(2n)!}{(3n)!}x^n$

Rewriting a double summation.

Prove area using simple sums and given sum

Show that $\sum_{k=0}^\infty \frac{e^{-x}(k-x)^2x^k}{k!} = x$

Is it possible to express this sum in a closed form?

Summing discrete coordinate lengths, a generalized n-dimensional case

How to evaluate $\sum\limits_{n=0}^\infty n^3x^n$, for $x\in[0,1)$.

Calculating Bernstein polynomial for function $x^3$.

find a closed form expression for $\sum_{k=0}^n \left \lceil\sqrt{2k} \right\rceil, \quad n \ge 0$

$x,y,z>0$, prove:$\frac{x}{y+z+\sqrt[4]\frac{y^4+z^4}{2}}+\frac{y}{z+x+\sqrt[4]\frac{z^4+x^4}{2}}+\frac{z}{x+y+\sqrt[4]\frac{x^4+y^4}{2}}\geq1$

Does $\lim_{x \to 1^{-}} \sum_{n=0}^{\infty} (x^n - x^{n+1})\log{(1+x^{n+1})} = 0$?

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