9.4 Day 2 Limit Comparison Test

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Presentation transcript:

9.4 Day 2 Limit Comparison Test

Limit Comparison Test If and for all (N a positive integer) If , then both and converge or both diverge. If , then converges if converges. If , then diverges if diverges.

Example 3a: When n is large, the function behaves like: harmonic series Since diverges, the series diverges.

Example 3b: When n is large, the function behaves like: geometric series Since converges, the series converges.

Use the limit comparison test to see if the series converges

Use the limit comparison test to see if the series converges Compare to This series converges It is a p-series Therefore the two series have the same growth rate. They both converge

Tests we know so far: Try this test first nth term test (for divergence only) Then try these Special series: Geometric, P series, Telescoping General tests: Direct comparison test, Limit comparison test, Integral test, Absolute convergence test (to be used with another test)

Homework p. 63015-27 odd 29-36 all Mother: Does your teacher like you ? Son: Like me, she loves me. Look at all those Xs on my test paper ! Q: What did one math book say to the other? A: Man I got a lot of problems!