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## Homework Statement

Find sequence [tex](a_n)[/tex] s.t. [tex]\lim_{N\rightarrow \infty} \sum_{n=1}^{2N} a_n[/tex] and [tex]\lim_{N\rightarrow \infty} \sum_{n=1}^{2N+1} a_n[/tex] both converge but [tex]\sum_{n=1}^{\infty} a_n[/tex] diverges.

I have no idea where to start to be honest. I'm confused at how this is possible. Isn't it always just summed to infinity regardless of whether it's 2(x) or 2(x+1) where x-> infinity?