Question

Write the integrand as a power series. Use this to evaluate the indefinite integral as a series. 2*integral[((e^x)-1)/(7x)] dx. Please help! Ty

Answer 1

Those are the options

Answer 2

This is how I tried to do it, but I think my manipulation is wrong.

Answer 3

The series of the exponential starts at 0: \(e^x = \sum_{k=0}^\infty \frac{x^k}{k!}\).
So \((e^x-1)/7x\) is \(\frac 17 \sum_{k=1}^\infty \frac{x^{k-1}}{k!}\).

Answer 4

oh, you didn't get it wrong for the "start at zero" remark, my bad.
I think the answer is C.

Answer 5

Thank you! Do you might telling me what I did wrong. Since there was a -1 on the left side of the equation, i added a -1 on the right… was this wrong?

Answer 6

This was wrong indeed. The effect of the "-1" is to change the n=0 to n=1 in the sum.

Answer 7

oh yeah! I get it now! :) Thank you!