Sum of series 0.5^(n)

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n = 1

\sum_{n=1}^{\infty} \left(\frac{1}{2}\right)^{n}

Sum((1/2)^n, (n, 1, oo))

The radius of convergence of the power series

Given number:

\left(\frac{1}{2}\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} = -2

d = -1

c = 0

then

\frac{1}{R} = \tilde{\infty} \left(-2 + \lim_{n \to \infty} 1\right)

False

R = 0

The rate of convergence of the power series

The answer [src]

1

Numerical answer [src]

1.00000000000000000000000000000

1.00000000000000000000000000000

The graph