Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
QUESTION
What is the interval of convergence of ##sum (x^(2n) )/( (2n)! )##?
For all ##x in RR##
We know that
##e^x = sum_k x^k/(k!)##
and that
##e^x + e^(-x) = 2sum_k x^(2k)/((2k)!) = 2cosh(x)##
so
##sum_k x^(2k)/((2k)!) = cosh(x)## which converges
for all ##x in RR##
