# Is the series #\sum_(n=1)^\infty((-5)^(2n))/(n^2 9^n)# absolutely convergent, conditionally convergent or divergent?

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(Use the appropriate test)

(Use the appropriate test)

The given series (\sum_{n=1}^\infty \frac{(-5)^{2n}}{n^2 9^n}) is absolutely convergent.

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Diverges by the Ratio Test.

The Ratio Test tells us we take

Then,

Thus,

We can factor these constants outside of the limit, getting

We dropped the absolute value bars as everything is positive when we go to infinity.

We also then have divergence by the Ratio Test.

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