Sum of series 1/4^1

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n = 1

\sum_{n=1}^{\infty} \left(\frac{1}{4}\right)^{1}

Sum((1/4)^1, (n, 1, oo))

The radius of convergence of the power series

Given number:

\left(\frac{1}{4}\right)^{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} = \frac{1}{4}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The rate of convergence of the power series

The answer [src]

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\infty

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Numerical answer

The series diverges

The graph