Sum of series 2i+1

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  oo           
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  )   (2*i + 1)
 /_,           
i = 1

\sum_{i=1}^{\infty} \left(2 i + 1\right)

Sum(2*i + 1, (i, 1, oo))

The radius of convergence of the power series

Given number:

2 i + 1

It is a series of species

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

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

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

In this case

a_{i} = 2 i + 1

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{i \to \infty}\left(\frac{2 i + 1}{2 i + 3}\right)

True

False

The rate of convergence of the power series

The answer [src]

oo

\infty

oo

Numerical answer

The series diverges

The graph