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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.

gt6989b
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jimm
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  • Finding a way to represent your expression as a sum may help? – Tony Hellmuth May 28 '18 at 02:31
  • 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 02:46
  • 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 02:47
  • @fleablood i added more terms,is it clear now? – jimm May 28 '18 at 02:52
  • https://math.stackexchange.com/questions/336035/establish-convergence-of-the-series-1-frac12-frac13-frac14-fra?rq=1 – Keith McClary May 28 '18 at 02:58
  • You missed my point. Describe the series. That's an important part of figuring out how to solve it. But, no, it is not clear, so it's negative to 10. When is it positive. It's important for you to be able to describe in words what the series is. – fleablood May 28 '18 at 04:26
  • Hint. What is the largest term in each block. What is the size of each block. Does that give you an upper bound? – fleablood May 28 '18 at 04:28

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