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12(0.73)^(n-1)

Sum of series 12(0.73)^(n-1)



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The solution

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  oo               
____               
\   `              
 \            n - 1
  \      / 73\     
  /   12*|---|     
 /       \100/     
/___,              
n = 1              
$$\sum_{n=1}^{\infty} 12 \left(\frac{73}{100}\right)^{n - 1}$$
Sum(12*(73/100)^(n - 1), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$12 \left(\frac{73}{100}\right)^{n - 1}$$
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
$$a_{n} = 12 \left(\frac{73}{100}\right)^{n - 1}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty}\left(\left(\frac{73}{100}\right)^{- n} \left(\frac{73}{100}\right)^{n - 1}\right)$$
Let's take the limit
we find
False

False

False
The rate of convergence of the power series
The answer [src]
400/9
$$\frac{400}{9}$$
400/9
Numerical answer [src]
44.444444444444444444444444444
44.444444444444444444444444444
The graph
Sum of series 12(0.73)^(n-1)

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