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Sum of series/ x/(x-1)

Sum of series x/(x-1)

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  /   x - 1
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x = 2

\sum_{x=2}^{\infty} \frac{x}{x - 1}

Sum(x/(x - 1), (x, 2, oo))

The radius of convergence of the power series

Given number:

\frac{x}{x - 1}

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} = \frac{x}{x - 1}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{x \to \infty}\left(\frac{x^{2} \left|{\frac{1}{x - 1}}\right|}{x + 1}\right)

True

False

The rate of convergence of the power series

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oo

\infty

oo

Numerical answer

The series diverges

The graph