Sum of series xi-yi

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  oo             
 __              
 \ `             
  )   (x*i - y*i)
 /_,             
i = 1

\sum_{i=1}^{\infty} \left(i x - i y\right)

Sum(x*i - y*i, (i, 1, oo))

The radius of convergence of the power series

Given number:

i x - i y

It is a series of species

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

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

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

In this case

a_{i} = i x - i y

and

x_{0} = 0

d = 0

c = 1

then

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

True

False

The answer [src]

oo*x - oo*y

\infty x - \infty y

oo*x - oo*y