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  • Sum of series:
  • sin(n*x)
  • xn/(1+x)^n
  • cos(1/n) cos(1/n)
  • n*3^n+1 n*3^n+1

  • Identical expressions

  • xn/(one +x)^n
  • xn divide by (1 plus x) to the power of n
  • xn divide by (one plus x) to the power of n
  • xn/(1+x)n
  • xn/1+xn
  • xn/1+x^n
  • xn divide by (1+x)^n

  • Similar expressions

  • xn/(1-x)^n
Sum of series/ xn/(1+x)^n

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


∑
=

The solution

You have entered [src] 
  oo          
____          
\   `         
 \        n   
  \      x    
   )  --------
  /          n
 /    (1 + x) 
/___,         
n = 1
$$\sum_{n=1}^{\infty} \frac{x^{n}}{\left(x + 1\right)^{n}}$$ 
Sum(x^n/(1 + x)^n, (n, 1, oo))
The answer [src] 
/         x               |  x  |    
|-------------------  for |-----| < 1
|        /      x  \      |1 + x|    
|(1 + x)*|1 - -----|                 
|        \    1 + x/                 
|                                    
<  oo                                
| ___                                
| \  `                               
|  \    n        -n                  
|  /   x *(1 + x)        otherwise   
| /__,                               
\n = 1
$$\begin{cases} \frac{x}{\left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)} & \text{for}\: \left|{\frac{x}{x + 1}}\right| < 1 \\\sum_{n=1}^{\infty} x^{n} \left(x + 1\right)^{- n} & \text{otherwise} \end{cases}$$ 
Piecewise((x/((1 + x)*(1 - x/(1 + x))), Abs(x/(1 + x)) < 1), (Sum(x^n*(1 + x)^(-n), (n, 1, oo)), True))

    Examples of finding the sum of a series

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