Mister Exam

Other calculators

Sum of series/ 1/(x*ln(x)^2)

Sum of series 1/(x*ln(x)^2)


∑
=

The solution

You have entered [src] 
  oo           
____           
\   `          
 \        1    
  \   ---------
  /        2   
 /    x*log (x)
/___,          
n = 2
$$\sum_{n=2}^{\infty} \frac{1}{x \log{\left(x \right)}^{2}}$$ 
Sum(1/(x*log(x)^2), (n, 2, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{x \log{\left(x \right)}^{2}}$$
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
$$a_{n} = \frac{1}{x \log{\left(x \right)}^{2}}$$
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 answer [src] 
    oo   
---------
     2   
x*log (x)
$$\frac{\infty}{x \log{\left(x \right)}^{2}}$$ 
oo/(x*log(x)^2)

    Examples of finding the sum of a series

    © Mister Exam – Calculator