Sum of series 1/(n*(n-1))

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  oo           
 ___           
 \  `          
  \       1    
   )  ---------
  /   n*(n - 1)
 /__,          
n = 2

\sum_{n=2}^{\infty} \frac{1}{n \left(n - 1\right)}

Sum(1/(n*(n - 1)), (n, 2, oo))

The radius of convergence of the power series

Given number:

\frac{1}{n \left(n - 1\right)}

It is a series of species

a_{n} \left(c x - x_{0}\right)^{d n}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}

In this case

a_{n} = \frac{1}{n \left(n - 1\right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\left(n + 1\right) \left|{\frac{1}{n - 1}}\right|\right)

True

False

The rate of convergence of the power series

The answer [src]

1

Numerical answer [src]

1.00000000000000000000000000000

1.00000000000000000000000000000

The graph