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Sum of series/ 1/(10^(4n-1))

Sum of series 1/(10^(4n-1))

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  oo           
____           
\   `          
 \        1    
  \   ---------
  /     4*n - 1
 /    10       
/___,          
n = 0

\sum_{n=0}^{\infty} \frac{1}{10^{4 n - 1}}

Sum(1/(10^(4*n - 1)), (n, 0, oo))

The radius of convergence of the power series

Given number:

\frac{1}{10^{4 n - 1}}

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} = 10^{1 - 4 n}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(10^{1 - 4 n} 10^{4 n + 3}\right)

False

False

The rate of convergence of the power series

The answer [src]

100000
------
 9999

\frac{100000}{9999}

100000/9999

Numerical answer [src]

10.0010001000100010001000100010

10.0010001000100010001000100010

The graph