(a) Find a function that represents the power series \displaystyle \sum_{k=0}^{\infty} 3(k+1)x^k.

k=0

?

?

?3(k+1)xk

. As always, show all work. [Hint: Split it.]

(b) Use your answer from (a) to find the sum of the series \displaystyle \sum_{k=0}^{\infty} \dfrac{3(k+1)\cdot 2^k}{5^k}.

k=0

?

?

?5k

3(k+1)?2k

your answer as a reduced fraction.

Q3 Problem 2 10 Points (a) Find a function that represents the power series E 3(k + 1)a* . As always, show all k=0 work. [Hint: Split it.] (b) Use your answer from (a) to find the sum of the series y 3(k + 1) . 2k 5k . Write your k=0 answer as a reduced fraction. Please select file(s) Select file(s)