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Sum of series/ (3/4)^n

Sum of series (3/4)^n

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  oo      
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  \      n
  /   3/4 
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n = 1

\sum_{n=1}^{\infty} \left(\frac{3}{4}\right)^{n}

Sum((3/4)^n, (n, 1, oo))

The radius of convergence of the power series

Given number:

\left(\frac{3}{4}\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{3}{4}

d = 1

c = 0

then

False

False

The rate of convergence of the power series

The answer [src]

3

Numerical answer [src]

3.00000000000000000000000000000

3.00000000000000000000000000000

The graph