STMATH126 (Calculus 3) Exam 1 Flashcards (Conditions & Results)

Geometric Series Convergence Condition

r<1

Geometric Series Divergence Condition

r>1

Sum of a Geometric Series

a/(1-r)

Divergence Test Divergence Condition

The limit of the series isn’t zero

Divergence Test Inconclusive Condition

The limit of the series is zero

Integral Test Conditions

Function is continuous, positive, decreasing for x greater than or equal to 1

Integral Test Convergence Condition

The integral converges

Integral Test Divergence Condition

The integral diverges

P-series Divergence Condition

p<=1

P-series Convergence Condition

p>1

Comparison Test Convergence Condition

Less than a known convergent series

Comparison Test Divergence Condition

Greater than a known divergent series

Limit Comparison Test Convergence Condition

Limit is 0 and known series converges

Limit Comparison Test Divergence Condition

Limit is infinite and known series diverges

Limit Comparison Test Result Interpretation

Finite positive limit that diverges or converges with known series

Alternating Series Test Convergence Condition

Series is nonincreasing and limit is 0

Ratio/Root Test Convergence Condition

Absolute limit is positive and less than 1

Ratio/Root Test Divergence Condition

Absolute limit is greater than 1

Ratio/Root Test Inconclusive Condition

Absolute limit equals 1