Sum of series 7+k

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  oo         
 __          
 \ `         
  )   (7 + k)
 /_,         
k = 1

\sum_{k=1}^{\infty} \left(k + 7\right)

Sum(7 + k, (k, 1, oo))

The radius of convergence of the power series

Given number:

k + 7

It is a series of species

a_{k} \left(c x - x_{0}\right)^{d k}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{x_{0} + \lim_{k \to \infty} \left|{\frac{a_{k}}{a_{k + 1}}}\right|}{c}

In this case

a_{k} = k + 7

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{k \to \infty}\left(\frac{k + 7}{k + 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