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Sum of series/ x^-6

Sum of series x^-6


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The solution

You have entered [src] 
  oo    
____    
\   `   
 \    1 
  \   --
  /    6
 /    x 
/___,   
n = 1
∑n=1∞1x6\sum_{n=1}^{\infty} \frac{1}{x^{6}} 
Sum(x^(-6), (n, 1, oo))
The radius of convergence of the power series
Given number:
1x6\frac{1}{x^{6}}
It is a series of species
an(cx−x0)dna_{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:
Rd=x0+lim⁡n→∞∣anan+1∣cR^{d} = \frac{x_{0} + \lim_{n \to \infty} \left|{\frac{a_{n}}{a_{n + 1}}}\right|}{c}
In this case
an=1x6a_{n} = \frac{1}{x^{6}}
and
x0=0x_{0} = 0
,
d=0d = 0
,
c=1c = 1
then
1=lim⁡n→∞11 = \lim_{n \to \infty} 1
Let's take the limit
we find
True

False
The answer [src] 
oo
--
 6
x
∞x6\frac{\infty}{x^{6}} 
oo/x^6

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