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  • Similar expressions

  • 1/3^(2x+1)
Sum of series/ 1/3^(2x-1)

Sum of series 1/3^(2x-1)


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The solution

You have entered [src] 
  oo          
 ___          
 \  `         
  \    1 - 2*x
  /   3       
 /__,         
n = 1
$$\sum_{n=1}^{\infty} \left(\frac{1}{3}\right)^{2 x - 1}$$ 
Sum((1/3)^(2*x - 1), (n, 1, oo))
The radius of convergence of the power series
Given number:
$$\left(\frac{1}{3}\right)^{2 x - 1}$$
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
$$a_{n} = \left(\frac{1}{3}\right)^{2 x - 1}$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
    1 - 2*x
oo*3
$$\infty 3^{1 - 2 x}$$ 
oo*3^(1 - 2*x)

    Examples of finding the sum of a series

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