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

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


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The solution

You have entered [src] 
  oo           
____           
\   `          
 \        n + 1
  \   (-1)     
  /   ---------
 /        n    
/___,          
n = 1
$$\sum_{n=1}^{\infty} \frac{\left(-1\right)^{n + 1}}{n}$$ 
Sum((-1)^(n + 1)/n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\left(-1\right)^{n + 1}}{n}$$
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
$$a_{n} = \frac{\left(-1\right)^{n + 1}}{n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{n + 1}{n}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
The answer [src] 
log(2)
$$\log{\left(2 \right)}$$ 
log(2)
Numerical answer [src] 
0.693147180559945309417232121458
0.693147180559945309417232121458
The graph
Sum of series (-1)^(n+1)/n

    Examples of finding the sum of a series

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