Mister Exam

Other calculators

Sum of series/ (1/(nsin(1/n)))

Sum of series (1/(nsin(1/n)))


∑
=

The solution

You have entered [src] 
  oo          
____          
\   `         
 \       1    
  \   --------
   )       /1\
  /   n*sin|-|
 /         \n/
/___,         
k = 1
$$\sum_{k=1}^{\infty} \frac{1}{n \sin{\left(\frac{1}{n} \right)}}$$ 
Sum(1/(n*sin(1/n)), (k, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{n \sin{\left(\frac{1}{n} \right)}}$$
It is a series of species
$$a_{k} \left(c x - x_{0}\right)^{d k}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{k \to \infty} \left|{\frac{a_{k}}{a_{k + 1}}}\right|}{c}$$
In this case
$$a_{k} = \frac{1}{n \sin{\left(\frac{1}{n} \right)}}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{k \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
   oo   
--------
     /1\
n*sin|-|
     \n/
$$\frac{\infty}{n \sin{\left(\frac{1}{n} \right)}}$$ 
oo/(n*sin(1/n))

    Examples of finding the sum of a series

    © Mister Exam – Calculator