Mister Exam

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Sum of series 1/(x+2)^5

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  oo           
____           
\   `          
 \        1    
  \    --------
  /           5
 /     (x + 2) 
/___,          
n = -1

\sum_{n=-1}^{\infty} \frac{1}{\left(x + 2\right)^{5}}

Sum(1/((x + 2)^5), (n, -1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{\left(x + 2\right)^{5}}

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(x + 2\right)^{5}}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The answer [src]

   oo   
--------
       5
(2 + x)

\frac{\infty}{\left(x + 2\right)^{5}}

oo/(2 + x)^5