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Sum of series/ 2/(10^(4n+1))

Sum of series 2/(10^(4n+1))

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  oo           
____           
\   `          
 \        2    
  \   ---------
  /     4*n + 1
 /    10       
/___,          
n = 1

\sum_{n=1}^{\infty} \frac{2}{10^{4 n + 1}}

Sum(2/10^(4*n + 1), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{2}{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} = 2 \cdot 10^{- 4 n - 1}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(10^{- 4 n - 1} \cdot 10^{4 n + 5}\right)

False

False

The rate of convergence of the power series

The answer [src]

1/49995

\frac{1}{49995}

1/49995

Numerical answer [src]

0.0000200020002000200020002000200020

0.0000200020002000200020002000200020

The graph