# Analysis Series Question

I'am having problems solving this question and would just like a hint on how to go about solving it because I have gotten no where.

The question goes like this: Using the steps below, show that the following sequence converges: $$1+ 1/2 - 2/3 + 1/4 + 1/5- 2/6 + 1/7 + 1/8 - 2/9 + 1/10 + 1/11 - 2/12++-++-...$$

Consider the subsequence (s2, s3, s5, s6, s8, s9, ...) of the sequence of partial sums. Show that this is the sequence of partial sums of a related convergent series.

Thanks

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Compute s2, s3, s5, s6, s8, s9. Do you see a pattern? – mathematician Jan 20 '14 at 19:56

$$\frac1{3n+1}+\frac1{3n+2}-\frac2{3n+3}=\frac2{(3n+1)(3n+3)}+\frac1{(3n+2)(3n+3)}\sim\frac1{3n^2}$$