Let be a series of positive terms. Find expressions for and , i.e. the th and the th term, and form the ratio . Determine the limiting value of this ratio as .
If , the series converges
If , the series diverges
If , the series may converge or diverge and the test gives us no definite information
Example Question 1
Test the series
We first all decide on the pattern of the terms and hence write down the th term. In this case . The th term will then be the same with replaced by
We now have to find the limiting value of the ratio as .
Because in this case, , we know that the given series is .