Mister Exam

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Sum of series:
cos(n)/n
n^(2n)/n!
1/n^3
sin(nx)
Identical expressions
n^(2n)/n!
n to the power of (2n) divide by n!
n(2n)/n!
n2n/n!
n^2n/n!
n^(2n) divide by n!

Sum of series/ n^(2n)/n!

Sum of series n^(2n)/n!

The solution

You have entered [src]

  oo      
____      
\   `     
 \     2*n
  \   n   
  /   ----
 /     n! 
/___,     
n = 0

$$\sum_{n=0}^{\infty} \frac{n^{2 n}}{n!}$$

Sum(n^(2*n)/factorial(n), (n, 0, oo))

The rate of convergence of the power series

The graph

Sum of series n^(2n)/n!

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
```