Mister Exam

Other calculators

  • How to use it?

  • Sum of series:
  • i^n
  • sen(ix)
  • 2^k 2^k
  • 256 256

  • Identical expressions

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

  • Similar expressions

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

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


∑
=

The solution

You have entered [src] 
  oo           
____           
\   `          
 \       n - 1 
  \     x      
  /   ---------
 /    n*(n + 1)
/___,          
n = 1
$$\sum_{n=1}^{\infty} \frac{x^{n - 1}}{n \left(n + 1\right)}$$ 
Sum(x^(n - 1)/((n*(n + 1))), (n, 1, oo))
The answer [src] 
/1   (2 - 2*x)*log(1 - x)              
|- + --------------------  for |x| <= 1
|x              2                      
|            2*x                       
|                                      
|      oo                              
|    ____                              
<    \   `                             
|     \         n                      
|      \       x                       
|       )  ----------       otherwise  
|      /            2                  
|     /    n*x + x*n                   
|    /___,                             
\    n = 1
$$\begin{cases} \frac{1}{x} + \frac{\left(2 - 2 x\right) \log{\left(1 - x \right)}}{2 x^{2}} & \text{for}\: \left|{x}\right| \leq 1 \\\sum_{n=1}^{\infty} \frac{x^{n}}{n^{2} x + n x} & \text{otherwise} \end{cases}$$ 
Piecewise((1/x + (2 - 2*x)*log(1 - x)/(2*x^2), |x| <= 1), (Sum(x^n/(n*x + x*n^2), (n, 1, oo)), True))

    Examples of finding the sum of a series

    © Mister Exam – Calculator