Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
nx^n!
(937/40-307/10)^2/18
x^n/(√(n+1)*4n)
x^factorial(n)
Limit of the function:
x^factorial(n)
Identical expressions
x^factorial(n)
x to the power of factorial(n)
xfactorial(n)
xfactorialn
x^factorialn

Sum of series/ x^factorial(n)

Sum of series x^factorial(n)

The solution

You have entered [src]

  oo     
 ___     
 \  `    
  \    n!
  /   x  
 /__,    
n = 1

$$\sum_{n=1}^{\infty} x^{n!}$$

Sum(x^factorial(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
```