Mister Exam

Other calculators

Sum of series/ log(n/n-2)

Sum of series log(n/n-2)


∑
=

The solution

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

    Examples of finding the sum of a series

    © Mister Exam – Calculator