#Calculus II - Power Series Problem

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errant geyser
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What I have done:

Step 1: I integrated the function f(x) to represent a geometric sequence, and found my values of a, r.

Step 2 is to differentiate F(x) in order to get back to f(x), and then finding my coefficients.

I get: 30^n-1 * nx ^ n-1 as my power series. What am I doing wrong?