Mister Exam

Other calculators

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

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


∑
=

The solution

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

    Examples of finding the sum of a series

    © Mister Exam – Calculator