AP Calculus BC Series Convergence Tests-solved

AP Calculus BC: Series Convergence
Tests



nth Term Test - Correct Answers -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.

Geometric Series Test - Correct Answers -If absolute value of r < 1, then series
converges.
If absolute value of r > 1, then series diverges.

P-Series Test - Correct Answers -If power > 1, then series converges.
If power < 1, then series diverges.

Integral Test - Correct Answers -If integral from 1 to infinity converges, then series
converges.
If integral from 1 to infinity diverges, then series diverges.

Ratio Test - Correct Answers -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.

Direct Comparison Test - Correct Answers -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.

Alternating Series Test - Correct Answers -Series converges if:
a) terms are decreasing AND positive.
b) limit of sequence equals 0.


Limit Comparison Test - Correct Answers -Converges if: