Finding b using power series for 1/(1+b)

[islandboy401]

Homework Statement

Problem: Find the value of b for which

Homework Equations

Power series for (1/1+x) or in this case, power series for (1/1+b)

The Attempt at a Solution

I keep getting ln (-5/6) as the answer, but apparently the correct answer is ln (5/6). I do not see why.

Please look at my work and tell me what I am doing wrong.

 

[dirk_mec1]

I can't see the problem.

 

[Mthees08]

Go back and write it out with the sums, limits, and ns in their proper places and I think you will see your error.