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Sum of series/ x*y

Sum of series x*y


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The solution

You have entered [src] 
  oo     
 __      
 \ `     
  )   x*y
 /_,     
n = 0
$$\sum_{n=0}^{\infty} x y$$ 
Sum(x*y, (n, 0, oo))
The radius of convergence of the power series
Given number:
$$x y$$
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
$$a_{n} = x y$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{n \to \infty} 1$$
Let's take the limit
we find
True

False
The answer [src] 
oo*x*y
$$\infty x y$$ 
oo*x*y

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