# Calc6.25

From Example Problems

Discuss the convergence or divergence of the series .

Let us compare this series with the geometric series .

If *r* < 1, then the series converges. If *r* > 1, then the series diverges. If *r* = 1, the ratio test is inconclusive, and the series may converge or diverge. Since in our case, *r* is equal to 1/3, the geometric series must converge.

Thus, since this limit is finite and positive, both series converge or diverge. Since the geometric series converges, then our series must also converge.