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(-1)n/2n-1

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



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The solution

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  oo             
 ___             
 \  `            
  \   /-n       \
   )  |---*n - 1|
  /   \ 2       /
 /__,            
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
$$1 = \lim_{n \to \infty}\left(\frac{\frac{n^{2}}{2} + 1}{\frac{\left(n + 1\right)^{2}}{2} + 1}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src]
-oo
$$-\infty$$
-oo
Numerical answer
The series diverges
The graph
Sum of series (-1)n/2n-1
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