Math 2300 Section 005 – Calculus II – Fall 2010
9.4 Limit Comparison Test Examples – October 6, 2010

Determine if the given series converges or diverges using the limit comparison test.
Solution: The dominant terms here are in the numerator and in the denominator. So, we compare the series terms
The terms form a convergent geometric series. And, we find that
Since we obtain a finite positive number using the limit comparison test, we know that both of the series either diverge or they both converge. We already knew that the series of terms converges, so the series in question must also converge.

Determine if the given series converges or diverges using the limit comparison test.
Solution: The dominant term in the numerator is , while the dominant term in the denominator is . So, we will attempt to compare this series to
which we know diverges.
Since the limit is finite and positive, we know that the original series diverges as well.