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
Have you checked the link?
Radius of convergence - Wikipedia, the free encyclopedia
See definition of Radius of convergence.