Mister Exam

Other calculators

Sum of series/ ln(1/x)

Sum of series ln(1/x)


∑
=

The solution

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

    Examples of finding the sum of a series

    © Mister Exam – Calculator