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AP Calculus BC: Series Convergence Tests

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Section 1

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nth Term Test

Front

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Calculus Math

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4 years ago

Date created

Mar 14, 2020

Cards (8)

Section 1

(8 cards)

nth Term Test

Front

If limit of SEQUENCE is NOT equal to 0, then SERIES diverges. If limit of SEQUENCE does equal zero, then SERIES COULD converge....not guaranteed.

Back

Ratio Test

Front

If the limit of the absolute value of "a sub (n+1)" over "a sub n" is < 1, then series converges. If the limit of the absolute value of "a sub (n+1)" over "a sub n" is > 1, then series converges. Test is inconclusive if it equals 1! Try another test.

Back

Limit Comparison Test

Front

Converges if: limit of "a sub n" over "b sub n" = a number greater than 0 AND the series of "b sub n" converges. Diverges if: limit of "a sub n" over "b sub n" = a number greater than 0 AND the series of "b sub n" diverges.

Back

Integral Test

Front

If integral from 1 to infinity converges, then series converges. If integral from 1 to infinity diverges, then series diverges.

Back

Alternating Series Test

Front

Series converges if: a) terms are decreasing AND positive. b) limit of sequence equals 0.

Back

Geometric Series Test

Front

If absolute value of r < 1, then series converges. If absolute value of r > 1, then series diverges.

Back

Direct Comparison Test

Front

Converges if: 0 is less than "a sub n" and that is less than or equal to "b sub n" AND series of "b sub n" converges. Diverges if: 0 is less than "b sub n" and that is less than or equal to "a sub n" AND series of "b sub n" diverges.

Back

P-Series Test

Front

If power > 1, then series converges. If power < 1, then series diverges.

Back