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Determine the convergence of the following series using the nth-partial sum or geometric series formula.

The sum of n=1 to inifitiy 1/(9n^2+3n-2)

How do I start? I'm guessing I should factor out the denominator but whats after that?

It is close to a geometric series, so use that test: the ratio of sucessive terms.

ratio= (9n^2+3n-2)/(9(n+1)^2 + 3(n+1) + 2)
and show it is less than one.

if it is geometric what is the sum of n?

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