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Sum of series/ 3/(n(n+2))

Sum of series 3/(n(n+2))

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  oo           
 ___           
 \  `          
  \       3    
   )  ---------
  /   n*(n + 2)
 /__,          
n = 1

\sum_{n=1}^{\infty} \frac{3}{n \left(n + 2\right)}

Sum(3/((n*(n + 2))), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{3}{n \left(n + 2\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{3}{n \left(n + 2\right)}

and

x_{0} = 0

d = 0

c = 1

then

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

True

False

The rate of convergence of the power series

The answer [src]

9/4

\frac{9}{4}

9/4

Numerical answer [src]

2.25000000000000000000000000000

2.25000000000000000000000000000

The graph