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Sum of series/ 1/(n(n-3))

Sum of series 1/(n(n-3))

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  oo           
 ___           
 \  `          
  \       1    
   )  ---------
  /   n*(n - 3)
 /__,          
n = 1

\sum_{n=1}^{\infty} \frac{1}{n \left(n - 3\right)}

Sum(1/(n*(n - 3)), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{n \left(n - 3\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 - 3\right)}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\frac{\left(n + 1\right) \left|{\frac{n - 2}{n - 3}}\right|}{n}\right)

True

False

The rate of convergence of the power series

The answer [src]

zoo

\tilde{\infty}

±oo

Numerical answer

The series diverges

The graph