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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 (sn) partial sums converges to L (finite). Then we say the series converges to L or has sum L. If (sn) 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 an > bn. So I haven't been able to find a suitable divergent sequence.
So basically we need a sequence bn 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 bn must of course be divergent
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