Mister Exam

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Sum of series:
n^2*sin(5/(3^n))
n*2^n
n^(1/n)
(n^2+5)/2^n
Identical expressions
n^(n+ one)/(n+ one)!
n to the power of (n plus 1) divide by (n plus 1)!
n to the power of (n plus one) divide by (n plus one)!
n(n+1)/(n+1)!
nn+1/n+1!
n^n+1/n+1!
n^(n+1) divide by (n+1)!
Similar expressions
n^(n-1)/(n+1)!
n^(n+1)/(n-1)!

Sum of series/ n^(n+1)/(n+1)!

Sum of series n^(n+1)/(n+1)!

The solution

You have entered [src]

  oo          
____          
\   `         
 \      n + 1 
  \    n      
  /   --------
 /    (n + 1)!
/___,         
n = 1

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

Sum(n^(n + 1)/factorial(n + 1), (n, 1, oo))

The rate of convergence of the power series

The graph

Sum of series n^(n+1)/(n+1)!

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
```