Is the series #\sum_(n=1)^\infty((-5)^(2n))/(n^2 9^n)# absolutely convergent, conditionally convergent or divergent?
(Use the appropriate test)
(Use the appropriate test)
1 Answer
Diverges by the Ratio Test.
Explanation:
We'll check for Absolute Convergence using the Ratio Test, where
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.