Sum of series -1n/2n-1

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

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```
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```
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```
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```
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```
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```
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```
Exam the series for convergence
```
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```

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Identical expressions

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Sum of series -1n/2n-1

The solution

Examples of finding the sum of a series