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lgn/lnn+2
Sum of series/ lgn/lnn+2

Sum of series lgn/lnn+2


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The solution

You have entered [src] 
  oo              
 ___              
 \  `             
  \   /log(n)    \
   )  |------ + 2|
  /   \log(n)    /
 /__,             
n = 1
$$\sum_{n=1}^{\infty} \left(2 + \frac{\log{\left(n \right)}}{\log{\left(n \right)}}\right)$$ 
Sum(log(n)/log(n) + 2, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$2 + \frac{\log{\left(n \right)}}{\log{\left(n \right)}}$$
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
$$a_{n} = 3$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
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 lgn/lnn+2

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