Use part (a) to find a power series for the following function. f(x)= (2+x) 3
1
​
2
1
​
∑ n=1
[infinity]
​
(−1) n
(n+2)(n+1) 2 n+3
x n
​
2
1
​
∑ n=0
[infinity]
​
(−1) n
(n+2)(n+1) 2 n+3
x n
​
∑ n=0
[infinity]
​
2 n
(n+2)(n+1) 2 n+3
x n
​
2∑ n=1
[infinity]
​
(−1) n
(n+3)(n+2)(n+1) 2 n+2
x n
​
2
1
​
∑ n=0
[infinity]
​
(−1) n
(n+1)n 2 n+2
x n
​
What is the radius of convergence? R= (c) Use part (b) to find a power series for the following function. f(x)= (2+x) 3
x 2
​
∑ n=0
[infinity]
​
(−1) n
(n+1)n 2 n+1
x n
​
2∑ n=2
[infinity]
​
(−1) n+1
n(n−1) 2 n+3
x n
​
2
1
​
∑ n=2
[infinity]
​
(−1) n
n(n−1) 2 n+1
x n
​
2
1
​
∑ n=1
[infinity]
​
(−1) n
n 2 n+2
x n
​
∑ n=2
[infinity]
​
2 n
n(n−1) 2 n+1
x 2n
​
What is the radius of convergence?