1. Find the center, radius and interval of convergence of the following series

a) sum n = 1 to ∞ (3 ^ (n + 1) * (x - 7) ^ n)/n

b) sum n = 1 to ∞ (2 * (4x + 1) ^ n)/(n ^ 2)

d) sum n = 1 to ∞ ((- 1) ^ (n + 1) * (x - 1) ^ n)/n

e) sum n = 1 to ∞ (2 ^ n * (4x - B) ^ n)/n

c) sum n = 1 to ∞ ((- 1) ^ n * (x - 2) ^ (2n + 1))/n

2. Find the power series representation for the following functions and determine their interval of convergence

a) f(x) = (x ^ 3)/(x + 2)

b) f(x) = (x ^ 2)/(a ^ 3 + x ^ 3)

3.) Find the Maclaurine series of the following functions.

a) f(x) = e ^ (3x)

b) f(x) = 2x ^ 3 * e ^ (- 2x ^ 2)

4. Use the binomial series and expand the given function as power series.

a. f(x) = 1/((1 + x) ^ 3)

b. f(x) = 1/((3 + x) ^ 4)

c. f(x) = (2x - 3) ^ 4