- #1

elliotician

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## Homework Statement

Determine whether the following series converges:

[tex]

\sum \frac{(n-1)^3}{\sqrt{n^8+n+2}}

[/tex]

## Homework Equations

Definition of convergence:

Let [tex]\sum a_{n}[/tex] be a series.

If the sequence of (s

_{n}) partial sums converges to L (finite). Then we say the series converges to L or has sum L. If (s

_{n}) diverges we say [tex]\sum a_{n}[/tex] diverges.

## The Attempt at a Solution

With some manipulation i can see the sequence acts like 1/n, thus the series [tex]\sum a_{n}[/tex] would diverge. However i can't use 1/n as a comparison since we would not have a

_{n}> b

_{n}. So I haven't been able to find a suitable divergent sequence.

So basically we need a sequence b

_{n}such:

[tex]\frac{(n-1)^3}{\sqrt{n^8+n+2}}}>b_{n}[/tex]

This doesn't need to hold for all natural numbers n we can have it for some n>=a.

And b

_{n}must of course be divergent

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