Mister Exam

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Sum of series:
(2*n-1)/2^n
x^n/n^2
cos(1/n)
2
Identical expressions
factorial(n)^ two /factorial(k^n)
factorial(n) squared divide by factorial(k to the power of n)
factorial(n) to the power of two divide by factorial(k to the power of n)
factorial(n)2/factorial(kn)
factorialn2/factorialkn
factorial(n)²/factorial(k^n)
factorial(n) to the power of 2/factorial(k to the power of n)
factorialn^2/factorialk^n
factorial(n)^2 divide by factorial(k^n)

Sum of series/ factorial(n)^2/factorial(k^n)

Sum of series factorial(n)^2/factorial(k^n)

The solution

You have entered [src]

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  \    n!  
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  /   / n\ 
 /    \k /!
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n = 1

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

Sum(factorial(n)^2/factorial(k^n), (n, 1, oo))

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
```