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0.4^n

Sum of series 0.4^n



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The solution

You have entered [src]
  oo      
 ___      
 \  `     
  \      n
  /   2/5 
 /__,     
n = 1     
$$\sum_{n=1}^{\infty} \left(\frac{2}{5}\right)^{n}$$
Sum((2/5)^n, (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(\frac{2}{5}\right)^{n}$$
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
$$x_{0} = - \frac{2}{5}$$
,
$$d = 1$$
,
$$c = 0$$
then
False

Let's take the limit
we find
False
The rate of convergence of the power series
The answer [src]
2/3
$$\frac{2}{3}$$
2/3
Numerical answer [src]
0.666666666666666666666666666667
0.666666666666666666666666666667
The graph
Sum of series 0.4^n
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