# Convergence of $1-\frac12-\frac13+\frac14+\frac15+\frac16-…$ [duplicate]

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.

• Perhaps see whether the blocks with constant sign decrease to zero? $1 > \frac{1}{2}+\frac{1}{3} > \frac{1}{4}+\frac{1}{5}+\frac{1}{6} \dots$ – GEdgar May 28 '18 at 2:46
• What series? why is $\frac 17$ subtracted but $\frac 16$ added? Is $\frac 18$ added or subtracted? After one $\frac 16$ what is the next term added. How do you determine when you add or subtract. – fleablood May 28 '18 at 2:47