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Sum of series/ 1/(2n-1)

Sum of series 1/(2n-1)

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  oo         
 ___         
 \  `        
  \      1   
   )  -------
  /   2*n - 1
 /__,        
n = 1

\sum_{n=1}^{\infty} \frac{1}{2 n - 1}

Sum(1/(2*n - 1), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{1}{2 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} = \frac{1}{2 n - 1}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty}\left(\left(2 n + 1\right) \left|{\frac{1}{2 n - 1}}\right|\right)

True

False

The rate of convergence of the power series

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oo

\infty

oo

Numerical answer

The series diverges

The graph