(1 point) Consider the following series: 1 1 1 " 1__ _7 _ _72 (__) _7"+... 5(x )+ 25 (x ) + + 5 (x ) Find the interval of convergence. The series converges if x is in (Enter your answer using interval notation.) Within the interval of convergence, find the sum of the series as a function of x. If x is in the interval of convergence, then the series converges to: Find the series obtained by differentiating the original series term by term. 00 The new series is 2 EEE n=0 (Since this sum starts at n = 0, be sure that your terms are of the form cnx" so as to avoid terms including negative exponents.) Find the interval of convergence of the new series. The new series converges if x is in 555 (Enter your answer using interval notation.) Within the interval of convergence, find the sum of the new series as a function of x. If x is in the interval of convergence, then the new series converges to: Find the series obtained by integrating the original series term by term. 00 The new series is 2 EEE n=0 Find the interval of convergence of the new series. The new series converges if x is in 5!! (Enter your answer using interval notation.) Within the interval of convergence, find the sum of the new series as a function of x. If x is in the interval of convergence, then the new series converges to