The ratio test gives you
giving you (-2,2), now check the end points.
Sum (-1)^n/(n 2^n) x^n
0. Find the interval of convergence of the power series defining f(x).
0. Find a power seies for f'(x) and determine its interval of convergence.
0. Find a power seies for integral 0 to x, f(t) dt and determine its interval of convergence.
any help would be appreciated!
Set up the Ratio Test.
which approaches
as n tends to infinity
Set this less than 1, then determine the radius and interval of convergence.
As to parts b) and c), there is a theorem that says that the radius of convergence remains the same for both the derivative and the antiderivative.
Good luck!