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(6)/(7^(n-2))
Sum of series/ (6)/(7^(n-2))

Sum of series (6)/(7^(n-2))


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The solution

You have entered [src] 
  oo        
____        
\   `       
 \      6   
  \   ------
  /    n - 2
 /    7     
/___,       
n = 1
$$\sum_{n=1}^{\infty} \frac{6}{7^{n - 2}}$$ 
Sum(6/7^(n - 2), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\frac{6}{7^{n - 2}}$$
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
$$a_{n} = 6 \cdot 7^{2 - n}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(7^{2 - n} 7^{n - 1}\right)$$
Let's take the limit
we find
False

False
The rate of convergence of the power series
The answer [src] 
49
$$49$$ 
49
Numerical answer [src] 
49.000000000000000000000000000
49.000000000000000000000000000
The graph
Sum of series (6)/(7^(n-2))

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