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Sum of series/ x+5

Sum of series x+5

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  oo         
 __          
 \ `         
  )   (x + 5)
 /_,         
x = 0

\sum_{x=0}^{\infty} \left(x + 5\right)

Sum(x + 5, (x, 0, oo))

The radius of convergence of the power series

Given number:

x + 5

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} = x + 5

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{x \to \infty}\left(\frac{x + 5}{x + 6}\right)

True

False

The rate of convergence of the power series

The answer [src]

oo

\infty

oo

Numerical answer

The series diverges

The graph