Infinite Sequences and Series · Superchallenge problem

The alternating harmonic series $\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}n$ converges to $\ln2$. Because it is only conditionally convergent, REARRANGING its terms can change the sum. If the terms are reordered by taking two positive terms then one negative term, repeating forever ($1,\tfrac13,-\tfrac12,\tfrac15,\tfrac17,-\tfrac14,\dots$), the new sum is known to equal $\tfrac32\ln2$. Find the exact value of (rearranged sum) $-$ (original sum).