Infinite Series Tests
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8 Terms
Test for Divergence
Divergent if the limit is non-zero or DNE
Geometric Series Test
ar^n. Divergent if abs(r) is greater than or equal to 1. Convergent if less than 1.
P-Series Test
1/n^p. Divergent if p less than or equal to 1. Convergent if greater than 1.
Ratio Test
Divergent if limit of n+1/n is greater than 1. Convergent if limit is less than 1.
Root test
Divergent if limit of nth root of an is greather than 1. Convergent if less than 1.
Direct Comparison Test
If bigger series converges, then smaller series converges. If smaller series diverges, then bigger series diverges.
Limit Comparison Test
If the limit of the quotient of two series is equal to some finite number, then they must both be either convergent or divergent.
Alternating Series Test
Convergent if the limit of the absolute value of an=0.