Sum of series (x-4)(x+4)

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  )   (x - 4)*(x + 4)
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x = 1

\sum_{x=1}^{\infty} \left(x - 4\right) \left(x + 4\right)

Sum((x - 4)*(x + 4), (x, 1, oo))

The radius of convergence of the power series

Given number:

\left(x - 4\right) \left(x + 4\right)

It is a series of species

a_{x} \left(c x - x_{0}\right)^{d x}

- power series.
The radius of convergence of a power series can be calculated by the formula:

R^{d} = \frac{x_{0} + \lim_{x \to \infty} \left|{\frac{a_{x}}{a_{x + 1}}}\right|}{c}

In this case

a_{x} = \left(x - 4\right) \left(x + 4\right)

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{x \to \infty}\left(\frac{\left(x + 4\right) \left|{\frac{x - 4}{x - 3}}\right|}{x + 5}\right)

True

False

The rate of convergence of the power series

Numerical answer

The series diverges

The graph