How Many Terms Are Needed to Estimate This Alternating Series Within 0.01?

[kuczmama]

Homework Statement

How many terms of the series
∞
Ʃ (-1)ⁿ/(ln(n+1))
n=1
are needed in order to estimate the exact sum within .01

Homework Equations

I know that I need to use the remainder estimate for the integral test where R_n=s-s_n

and that ∫ from (n+1) to ∞ of f(x)dx $\leq$ R_n $\leq$ ∫ from (n) to ∞ of f(x)dx

The Attempt at a Solution

I tried to take the integral but I don't know how, and I can't figure out another way to approach the problem

 

[LCKurtz]

I don't think you want to use an integral.

Hint: Don't you have a theorem for alternating series (with certain hypotheses) that compares the error to the first term not included?