Find the intervals of convergence for the function. f(x)=sum_(n=1)^infinity x**n/n**2 32324243232 incorrect: your answer is incorrect. (b) find the intervals of convergence for f '.

will converge as long as



according to the ratio test. We have



so the sum will certainly converge whenever , but we also know the series will converge at the endpoints. is a convergent -series, which means is also (absolutely) convergent, so in fact the interval of convergence is (endpoints included).