Consider the following series: 1− 4
1
(x−6)+ 16
1
(x−6) 2
+⋯+(− 4
1
) n
(x−6) n
+⋯ 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. The new series is ∑ n=0
[infinity]
(Since this sum starts at n=0, be sure that your terms are of the form c n
x n
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 (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. The new series is ∑ n=0
[infinity]
Find the interval of convergence of the new series. The new series converges if x is in (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: