Mister Exam

Other calculators

1/(x*(x+1))
Sum of series/ 1/(x*(x+1))

Sum of series 1/(x*(x+1))


∑
=

The solution

You have entered [src] 
  oo           
 ___           
 \  `          
  \       1    
   )  ---------
  /   x*(x + 1)
 /__,          
x = 1
$$\sum_{x=1}^{\infty} \frac{1}{x \left(x + 1\right)}$$ 
Sum(1/(x*(x + 1)), (x, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{x \left(x + 1\right)}$$
It is a series of species
$$a_{x} \left(c x - x_{0}\right)^{d x}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}$$
In this case
$$a_{x} = \frac{1}{x \left(x + 1\right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{x \to \infty}\left(\frac{x + 2}{x}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
1
$$1$$ 
1
Numerical answer [src] 
1.00000000000000000000000000000
1.00000000000000000000000000000
The graph
Sum of series 1/(x*(x+1))

    Examples of finding the sum of a series

    © Mister Exam – Calculator