Mister Exam

Other calculators

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

Sum of series 1/(ln^2x)


∑
=

The solution

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

    Examples of finding the sum of a series

    © Mister Exam – Calculator