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AP Calculus BC Series test

memorize.ai (lvl 286)

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Section 1

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Alternating series test

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Calculus Math

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Last updated

5 years ago

Date created

Mar 14, 2020

Cards (10)

Section 1

(10 cards)

Alternating series test

Front

(-1)^n or cos(pi x n) or sin(pi x n) or something like that it converges if it is alternating, decreasing in magnitude, and has a limit of a sub n equals 0 Not used to determine divergence

Back

nth term test

Front

When n probably doesn't equal zero Divergent if the limit as n goes to infinity does NOT equal zero Does not determine convergence

Back

Telescoping series

Front

Freeman's favorite Usually one fraction minus another, or you may have to separate it using partial fractions Converges if things cancel out

Back

Integral test

Front

Must be: continuous, positive, and decreasing

Back

Root Test

Front

Use when: (#)^n If its less than 1 it converges greater than 1 diverges =1 is inconclusive

Back

Ratio Test

Front

Use when it is ugly and there are nonzero terms If the comparable one converges and it works, then it converges If the comparable one diverges and it works, then they both diverge

Back

p-series test

Front

Back

Direct Comparison Test

Front

Use this when it is almost a nice p-series or geometric It converges if it is smaller than the comparable series that converges. It diverges if it is larger than the comparable series that diverges.

Back

Limit Comparison Test

Front

Use when direct comparison doesn't work or a ratio is given.

Back

Geometric series test

Front

Something is multiplied over and over The series of (r)^n converges if |r|<1 and diverges if |r|>1 or |r|=1

Back