# Analysis Question based on Series

I've been having some difficulty solving this question especially with understanding how to comput the specific subesequence specified and why they relate to solving this question.

The question is:

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.

So far I have considered a sequence (sn) of the partial sums such that

(sn) = ∑(1/3n+1 + 1/3n+2 - 2/3n+3) = 2/(3n+1)(3n+3) + 1/(3n+2)(3n+3) ~ 1/3n^2

but I am not sure of how to compute the specified subsequences from this.

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–  David Mitra Jan 22 at 13:56