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log(n+1)/(n+1)
Sum of series/ log(n+1)/(n+1)

Sum of series log(n+1)/(n+1)


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The solution

You have entered [src] 
  oo            
 ___            
 \  `           
  \   log(n + 1)
   )  ----------
  /     n + 1   
 /__,           
n = 1
$$\sum_{n=1}^{\infty} \frac{\log{\left(n + 1 \right)}}{n + 1}$$ 
Sum(log(n + 1)/(n + 1), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{\log{\left(n + 1 \right)}}{n + 1}$$
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
$$a_{n} = \frac{\log{\left(n + 1 \right)}}{n + 1}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\frac{\left(n + 2\right) \log{\left(n + 1 \right)}}{\left(n + 1\right) \log{\left(n + 2 \right)}}\right)$$
Let's take the limit
we find
True

False
The rate of convergence of the power series
Numerical answer
The series diverges
The graph
Sum of series log(n+1)/(n+1)

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