Mister Exam

Lang:

Other calculators

How to use it?
Sum of series:
((2*n+4)/(5*n+7))^n*x^n
x^n/(1+x^n)
(n-2^(3*n))/(n+1)^(1/3)
(-1)^(2n+1)*x^(2n+1)/(2n+1)!
Limit of the function:
x^n/(1+x^n)
Identical expressions
x^n/(one +x^n)
x to the power of n divide by (1 plus x to the power of n)
x to the power of n divide by (one plus x to the power of n)
xn/(1+xn)
xn/1+xn
x^n/1+x^n
x^n divide by (1+x^n)
Similar expressions
x^n/(1-x^n)

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

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

The solution

You have entered [src]

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

$$\sum_{n=1}^{\infty} \frac{x^{n}}{x^{n} + 1}$$

Sum(x^n/(1 + x^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
```