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1/((n+14)(n+15))
Sum of series/ 1/((n+14)(n+15))

Sum of series 1/((n+14)(n+15))


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The solution

You have entered [src] 
  oo                   
 ___                   
 \  `                  
  \           1        
   )  -----------------
  /   (n + 14)*(n + 15)
 /__,                  
n = 1
$$\sum_{n=1}^{\infty} \frac{1}{\left(n + 14\right) \left(n + 15\right)}$$ 
Sum(1/((n + 14)*(n + 15)), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{\left(n + 14\right) \left(n + 15\right)}$$
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
$$a_{n} = \frac{1}{\left(n + 14\right) \left(n + 15\right)}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{n + 16}{n + 14}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
1/15
$$\frac{1}{15}$$ 
1/15
Numerical answer [src] 
0.0666666666666666666666666666667
0.0666666666666666666666666666667
The graph
Sum of series 1/((n+14)(n+15))

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