How do i establish the convergence of the series
$$1-\frac12-\frac13+\frac14+\frac15+\frac16-\frac17-\frac18-\frac19-\frac1 {10}+...$$
where the number of signs increases by 1 in each "block"?
I cannot apply the Dirichlet test because the sequence of partial sums of $1,-1,-1,1,1,1,...$ is not bounded.
Please help.