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Sum of series/ (-1)^n/sqrt(n)

Sum of series (-1)^n/sqrt(n)

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  oo       
____       
\   `      
 \        n
  \   (-1) 
   )  -----
  /     ___
 /    \/ n 
/___,      
n = 1

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

Sum((-1)^n/sqrt(n), (n, 1, oo))

The radius of convergence of the power series

Given number:

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

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}{\sqrt{n}}

and

x_{0} = 1

d = 1

c = 0

then

R = \tilde{\infty} \left(1 + \lim_{n \to \infty}\left(\frac{\sqrt{n + 1}}{\sqrt{n}}\right)\right)

False

The rate of convergence of the power series

The graph