I'm not totally sure how to do this problem...

By grouping terms as appropriate show that $\frac{7}{12} \leq \sum\limits\_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} \leq \frac{47}{60}$

I've got that $\sum\limits\_{n=1}^{4} \frac{(-1)^{n+1}}{n} = \frac{7}{12}$

and $\sum\limits\_{n=1}^{5} \frac{(-1)^{n+1}}{n} = \frac{47}{60} $

And that, by the alternating series test, $\sum\limits\_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}$ converges. However, I'm not sure what it converges to and if that will uphold my inequality.

Thanks in advance!