5.11 Comparison & limit comparison test

Comparison & limit comparison test

Lessons

Notes:
Note *The Comparison test says the following:
Let an\sum a_n and bn\sum b_n be two series where anbna_n\leq b_n for all nn and anbn0a_nb_n\geq0. Then we say that
1. If bn\sum b_n is convergent, then an\sum a_n is also convergent
2. If an\sum a_n is divergent, then bn\sum b_n is also divergent.

The Limit Comparison Test says the following:
Let an\sum a_n and bn\sum b_n be two series where an0a_n\geq 0 and bnb_n > 0 for all nn. Then we say that

lim\limn →\infty anbn=c\frac{a_n}{b_n}=c

If cc is a positive finite number, then either both series converge or diverge.
  • 1.
    Overview:

  • 2.
    Convergence & Divergence of Comparison Tests
    Use the Comparison Test to determine if the series converge or diverge.
  • 3.
    Convergence & Divergence of Limit Comparison Tests
    Use the Limit Comparison Test to determine if the series converge or diverge.
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Comparison & limit comparison test

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