Try to write the sum with the form . I think we will have to use the result .
I have to prove that
1 + 1/3 - 1/2 + 1/5 + 1/7 - 1/4 + 1/9 + 1/11 - 1/6 + ...
converges to (3/2)ln2 (which is also equal to ln8/2 if it is easier to work with).
I have no idea what to do with this, as the alternating harmonic series has conditional and not absolute convergence. How would I go about actually proving this convergence?