Question

Prove $\lim\limits_{r \to \infty} r-\frac{\sqrt{r}}{e^{r}}\sum_{n=0}^{\infty}\frac{\Gamma{(n+3/2)}r^n}{(n!)^2}=1/4$

score 96 · Answer 1 · 2026-03-26 06:22:19

96

Views

Prove $\lim\limits_{r \to \infty} r-\frac{\sqrt{r}}{e^{r}}\sum_{n=0}^{\infty}\frac{\Gamma{(n+3/2)}r^n}{(n!)^2}=1/4$

Published on 26 Mar 2026 - 6:22

score 131 · Answer 2 · 2018-09-23 22:22:32

131

Views

An expression for the sum $\sum\limits _{k=1}^{n-1} k \, (n-k)^2$

Published on 23 Sep 2018 - 22:22

score 3.3k · Answer 3 · 2026-03-25 04:19:10

3.3k

Views

Why is $\sum_{i=1}^n a$ always irrational if $n>0$ and $a$ is irrational?

Published on 25 Mar 2026 - 4:19

score 755 · Answer 4 · 2018-09-24 17:19:04

755

Views

$\sum_{k=1}^{∞} k(1-p)^{k-1}+\sum_{k=1}^{∞} kp^{k-1}$ for $0 < p < 1$

Published on 24 Sep 2018 - 17:19

score 414 · Answer 5 · 2026-03-27 13:45:31

414

Views

Maximize a series

Published on 27 Mar 2026 - 13:45

score 225 · Answer 6 · 2026-03-26 08:04:39

225

Views

How to find a numerical approximation of this sum.

Published on 26 Mar 2026 - 8:04

score 428 · Answer 7 · 2026-03-27 17:04:32

428

Views

Proving $\sum_{i=1}^{n} {{n}\choose{i}} (-1)^i = -1$ by induction

Published on 27 Mar 2026 - 17:04

score 152 · Answer 8 · 2018-09-25 15:48:53

152

Views

How to Solve Summation Notation

Published on 25 Sep 2018 - 15:48

score 273 · Answer 9 · 2026-03-26 12:15:30

273

Views

Total Cost of List of Items

Published on 26 Mar 2026 - 12:15

score 1.1k · Answer 10 · 2026-03-27 17:04:25

1.1k

Views

What is the sum of the binomial coefficients ${n\choose p}$ over prime numbers?

Published on 27 Mar 2026 - 17:04

score 128 · Answer 11 · 2026-03-25 04:40:51

128

Views

What is the closed form of $\sum_{j=i}^{n} {j}$?

Published on 25 Mar 2026 - 4:40

score 1.8k · Answer 12 · 2026-03-27 17:04:57

1.8k

Views

Questions on a self-made theorem about polynomials

Published on 27 Mar 2026 - 17:04

score 6.7k · Answer 13 · 2026-03-26 02:49:02

6.7k

Views

Prove that the summation from n=0 to infinity of a^n is 1/(1-a)

Published on 26 Mar 2026 - 2:49

score 273 · Answer 14 · 2026-03-25 23:38:03

273

Views

Compute $\sum_{i=1}^n\frac i{\gcd(i,n)}$

Published on 25 Mar 2026 - 23:38

score 43 · Answer 15 · 2018-09-27 01:57:47

43

Views

How to solve this summation? from i+1 to n

Published on 27 Sep 2018 - 1:57

List Question

Prove $\lim\limits_{r \to \infty} r-\frac{\sqrt{r}}{e^{r}}\sum_{n=0}^{\infty}\frac{\Gamma{(n+3/2)}r^n}{(n!)^2}=1/4$

An expression for the sum $\sum\limits _{k=1}^{n-1} k \, (n-k)^2$

Why is $\sum_{i=1}^n a$ always irrational if $n>0$ and $a$ is irrational?

$\sum_{k=1}^{∞} k(1-p)^{k-1}+\sum_{k=1}^{∞} kp^{k-1}$ for $0 < p < 1$

Maximize a series

How to find a numerical approximation of this sum.

Proving $\sum_{i=1}^{n} {{n}\choose{i}} (-1)^i = -1$ by induction

How to Solve Summation Notation

Total Cost of List of Items

What is the sum of the binomial coefficients ${n\choose p}$ over prime numbers?

What is the closed form of $\sum_{j=i}^{n} {j}$?

Questions on a self-made theorem about polynomials

Prove that the summation from n=0 to infinity of a^n is 1/(1-a)

Compute $\sum_{i=1}^n\frac i{\gcd(i,n)}$

How to solve this summation? from i+1 to n

Trending Questions

Popular # Hahtags

Popular Questions