Mister Exam

Other calculators

Sum of series/ x^-6

Sum of series x^-6


∑
=

The solution

You have entered [src] 
  oo    
____    
\   `   
 \    1 
  \   --
  /    6
 /    x 
/___,   
n = 1
$$\sum_{n=1}^{\infty} \frac{1}{x^{6}}$$ 
Sum(x^(-6), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{1}{x^{6}}$$
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
$$a_{n} = \frac{1}{x^{6}}$$
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
--
 6
x
$$\frac{\infty}{x^{6}}$$ 
oo/x^6

    Examples of finding the sum of a series

    © Mister Exam – Calculator