Previous: Videos on the Integral Test
Next: The Alternating Series Test
Previous: Videos on the Integral Test
Next: The Alternating Series Test
Previous: Videos on the Integral Test
Next: The Alternating Series Test
The previous lesson on the divergence test gave us a way of determining whether some infinite series diverge. We saw that the divergence test had a limitation: it can tell us if certain infinite series diverges, but it cannot tell us if a given series converges. But there are other convergence tests. The integral test, for example, provides a test for any series
whose terms a_{n} can be related to a continuous, positive, decreasing function. Essentially, we let , then evaluate the integral
and:
Although this test is limited to functions who are continuous, positive and decreasing, we saw that it led us to a useful convergence theorem for any infinite series of the form
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