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Sum of series:
(1-5/n)^n
1/((2p)^2(2p-1)!(n-2p)!)
((125/9))((3/5)^n)
tan(1/2^n)/2^n
Identical expressions
one /((two p)^2(2p- one)!(n-2p)!)
1 divide by ((2p) squared (2p minus 1)!(n minus 2p)!)
one divide by ((two p) squared (2p minus one)!(n minus 2p)!)
1/((2p)2(2p-1)!(n-2p)!)
1/2p22p-1!n-2p!
1/((2p)²(2p-1)!(n-2p)!)
1/((2p) to the power of 2(2p-1)!(n-2p)!)
1/2p^22p-1!n-2p!
1 divide by ((2p)^2(2p-1)!(n-2p)!)
Similar expressions
1/((2p)^2(2p+1)!(n-2p)!)
1/((2p)^2(2p-1)!(n+2p)!)

Sum of series 1/((2p)^2(2p-1)!(n-2p)!)

The solution

You have entered [src]

  oo                              
____                              
\   `                             
 \                 1              
  \   ----------------------------
  /        2                      
 /    (2*p) *(2*p - 1)!*(n - 2*p)!
/___,                             
p = 1

$$\sum_{p=1}^{\infty} \frac{1}{\left(2 p\right)^{2} \left(2 p - 1\right)! \left(n - 2 p\right)!}$$

Sum(1/(((2*p)^2*factorial(2*p - 1))*factorial(n - 2*p)), (p, 1, oo))

The answer [src]

/                                                  
|   _  /          n  3   n |  \                    
|  |_  |1, 1, 1 - -, - - - |  |                    
|  |   |          2  2   2 | 1|                    
| 4  3 |                   |  |                    
|      \    3/2, 2, 2      |  /                    
| -----------------------------   for 1 + re(n) > 0
|         Gamma(-1 + n)                            
|                                                  
<  oo                                              
|____                                              
|\   `                                             
| \                1                               
|  \   -------------------------                   
|  /    2                             otherwise    
| /    p *(-1 + 2*p)!*(n - 2*p)!                   
|/___,                                             
|p = 1                                             
\                                                  
---------------------------------------------------
                         4

$$\frac{\begin{cases} \frac{{{}_{4}F_{3}\left(\begin{matrix} 1, 1, 1 - \frac{n}{2}, \frac{3}{2} - \frac{n}{2} \\ \frac{3}{2}, 2, 2 \end{matrix}\middle| {1} \right)}}{\Gamma\left(n - 1\right)} & \text{for}\: \operatorname{re}{\left(n\right)} + 1 > 0 \\\sum_{p=1}^{\infty} \frac{1}{p^{2} \left(n - 2 p\right)! \left(2 p - 1\right)!} & \text{otherwise} \end{cases}}{4}$$

Piecewise((hyper((1, 1, 1 - n/2, 3/2 - n/2), (3/2, 2, 2), 1)/gamma(-1 + n), 1 + re(n) > 0), (Sum(1/(p^2*factorial(-1 + 2*p)*factorial(n - 2*p)), (p, 1, oo)), True))/4

Examples of finding the sum of a series

The Sum of the Power Series
```
x^n/n
```
```
(x-1)^n
```
Factorial
```
1/2^(n!)
```
```
n^2/n!
```
```
x^n/n!
```
```
k!/(n!*(n+k)!)
```
Flint Hills Series
```
csc(n)^2/n^3
```
Basel problem
```
1/n^2
```
```
1/n^4
```
```
1/n^6
```
Harmonic series
```
1/n
```
Grandi's series
```
(-1)^n
```
Alternating series
```
(-1)^(n + 1)/n
```
```
(n + 2)*(-1)^(n - 1)
```
```
(3*n - 1)/(-5)^n
```
```
(-1)^(n - 1)*n/(6*n - 5)
```
Newton–Mercator series
```
(-1)^(n + 1)/n*x^n
```
Exam the series for convergence
```
(3*n - 1)/(-5)^n
```

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Identical expressions

Similar expressions

Sum of series 1/((2p)^2(2p-1)!(n-2p)!)

The solution

Examples of finding the sum of a series