Review of Convergence Tests

Front

nth term test: If the limit as n approaches infinity of a series is __________ zero, then the series will diverge.

Back

not equal to zero.

Front

Geometric Series: A geometric series will converge if __________.

Back

|r| < 1.

Front

Geometric Series: If a geometric series converges, the sum of the series will be equal to...

Back

Front

Integral test: If the integral __________ , then the series converges.

Back

converges.

Front

p-series: A p-series will converge if __________.

Back

p > 1.

Front

Definition of Convergence: A series converges if the sequence of its partial sums approaches a finite limit.

Back

Convergence means the sum approaches a specific value.

Front

Definition of Divergence: A series diverges if the sequence of its partial sums does not approach a finite limit.

Back

Divergence means the sum does not settle at a specific value.

Front

Comparison Test: If 0 ≤ a_n ≤ b_n and the series of b_n converges, then the series of a_n __________.

Back

converges.

Front

Limit Comparison Test: If the limit of a_n/b_n as n approaches infinity is a positive finite number, then both series either converge or diverge together.

Back

Use this test to compare two series.

Front

Ratio Test: A series converges absolutely if the limit of |a_{n+1}/a_n| < 1.

Back

Use this test to determine absolute convergence.