Mister Exam

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How to use it?
Sum of series:
9/(9n^2+21n-8)
(3-sin*n)/n-lnn
1/(1+n^2)
e^(-n)
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 minus x to the power of n)
x to the power of n divide by (one minus 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

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

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
```