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Sum of series/ 1/(8+x)

Sum of series 1/(8+x)

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  oo       
 ___       
 \  `      
  \     1  
   )  -----
  /   8 + x
 /__,      
x = 1

\sum_{x=1}^{\infty} \frac{1}{x + 8}

Sum(1/(8 + x), (x, 1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{x + 8}

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 + 8}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{x \to \infty}\left(\frac{x + 9}{x + 8}\right)

True

False

The rate of convergence of the power series

The answer [src]

oo

\infty

oo

Numerical answer

The series diverges

The graph