i having great problems trying to find the R= radius of convergence.

the qns is. show that R= infinity for the series exp(x) = 1+ x/1! + x^2 /2! +...

my working:

exp (x) = summation from n=0 to infinity (x^n)/n!

i cant think of a way how to make n start from 1 instead of 0.

so in this case, let a_n = 1/n!

then using ratio test, R = lim (a_n+1 / a_n) = 1/(n+1)

thus as n tends to infinity, R tends to 0... but i need to show that R= infinity