What is the interval of convergence of #sum_1^oo ((-1)^(n-1)*x^(n+1))/((n+1)!)#?
1 Answer
Apr 30, 2018
Use the ratio test to detmeurine the radius of convergence first:
#L = lim_(n-> oo) (((-1)^(n)x^(n + 2))/((n + 2)!))/(((-1)^(n - 1)x^(n + 1))/((n + 1)!)#
#L = lim_(n->oo) (-1(x))/(n + 2)#
Take the absolute value.
#L = |x|lim_(n->oo) 1/(n + 2)#
#L = |x| (0)#
#L = 0#
This converges for all values of
The interval of convergence is therefore
Hopefully this helps!