Sum of series x^y/y!

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  oo    
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\   `   
 \     y
  \   x 
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 /    y!
/___,   
n = 1

\sum_{n=1}^{\infty} \frac{x^{y}}{y!}

Sum(x^y/factorial(y), (n, 1, oo))

The radius of convergence of the power series

Given number:

\frac{x^{y}}{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} = \frac{x^{y}}{y!}

and

x_{0} = 0

d = 0

c = 1

then

1 = \lim_{n \to \infty} 1

True

False

The answer [src]

    y
oo*x 
-----
  y!

\frac{\infty x^{y}}{y!}

oo*x^y/factorial(y)