Estimate the sum of alternating harmonic series between $7/12$ and $47/60$ How can I prove that: 
$$\frac{7}{12} < \sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n} < \frac{47}{60}$$ 
? I don't even know how to start solving this... 

Hint your sum is integration of $\int (1+x)^{-1}$ after integration put $x=1$ . So series converges to $\ln(2)$
