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

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

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  oo             
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  \   /-n       \
   )  |---*n - 1|
  /   \ 2       /
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n = 1

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

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

The radius of convergence of the power series

Given number:

n \frac{\left(-1\right) n}{2} - 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{n^{2}}{2} - 1

and

x_{0} = 0

d = 0

c = 1

then

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

True

False

The rate of convergence of the power series

The answer [src]

-oo

-\infty

-oo

Numerical answer

The series diverges

The graph