Posted by Anonymous on Saturday, October 29, 2011 at 11:10pm.
I think it should help to notice that
5n^2 + 6n + 3 = 3n^2 + 6n + 3 + 2n^2 = 3(n+1)^2 + 2n^2
So, what you have is just
3/n^2 + 2/(n+1)^2
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