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(5/6)^n
Sum of series/ (5/6)^n

Sum of series (5/6)^n


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The solution

You have entered [src] 
  oo      
 ___      
 \  `     
  \      n
  /   5/6 
 /__,     
n = 0
∑n=0∞(56)n\sum_{n=0}^{\infty} \left(\frac{5}{6}\right)^{n} 
Sum((5/6)^n, (n, 0, oo))
The radius of convergence of the power series
Given number:
(56)n\left(\frac{5}{6}\right)^{n}
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=1a_{n} = 1
and
x0=−56x_{0} = - \frac{5}{6}
,
d=1d = 1
,
c=0c = 0
then
False

Let's take the limit
we find
False
The rate of convergence of the power series
0.06.00.51.01.52.02.53.03.54.04.55.05.505
The answer [src] 
6
66 
6
Numerical answer [src] 
6.00000000000000000000000000000
6.00000000000000000000000000000
The graph
Sum of series (5/6)^n

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