Mister Exam

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Sum of series:
(3/4)^n
1/((2n-1)*(2n+1))
1/(n*(n+3))
(5/6)^n
Limit of the function:
(5/6)^n
Identical expressions
(five / six)^n
(5 divide by 6) to the power of n
(five divide by six) to the power of n
(5/6)n
5/6n
5/6^n
(5 divide by 6)^n

Sum of series/ (5/6)^n

Sum of series (5/6)^n

The solution

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  oo      
 ___      
 \  `     
  \      n
  /   5/6 
 /__,     
n = 0

$$\sum_{n=0}^{\infty} \left(\frac{5}{6}\right)^{n}$$

Sum((5/6)^n, (n, 0, oo))

The radius of convergence of the power series

Given number:
$$\left(\frac{5}{6}\right)^{n}$$
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
$$a_{n} = 1$$
and
$$x_{0} = - \frac{5}{6}$$
,
$$d = 1$$
,
$$c = 0$$
then