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**[SOLVED] Approximating the "Tail" of a Series**

**1. Homework Statement**

I need to estimate the tail, which is

[tex]\Sigma[/tex] (from n=6 to infinity) (4-sin n)/(n^2+1)

It says to do this with an appropriate improper integral or geometric series.

**3. The Attempt at a Solution**

I don't see a geometric series helping here, so I would use an improper integral. It is too difficult to integrate (4-sin n)/(n^2+1) (if it's even possible), so I'm stuck here. If this can be integrated, please show me the way. I was thinking perhaps do an improper integral for series of 5/n^2 instead since that is always larger (i.e. if you write 4+/- 1)/(n^2+1) instead. Would this be appropriate?