CALCULUS 2 SERIES TESTS FULLY SOLVED -3.

CALCULUS 2 SERIES TESTS FULLY SOLVED #3
Test for Divergence - correct answer Series Type: ALL
When to try: First

Geometric Series - correct answer Series Type: Sum(1..Inf) a*r^(n-1)

Integral - correct answer Series type: f(n) is positive, continuous, decreasing
When to try: f(n) must be integrable

P-Series - correct answer Series type: Sum(1..Inf) 1/(n^p)

Direct Comparison - correct answer Series type: An and Bn are positive
When to try: If it looks close to a p-series or geometric

Limit Comparison - correct answer Series type: An and Bn are positive
When to try: if a Direct Comparison Test does not work

Alternating Series - correct answer Series type: Sum(1..Inf)(-1^(n-k))*Bn
* Use test for divergence if limit does not equal 0

Absolute convergence - correct answer Series type: ALL
When to try: With trig. Series or some alternating series

Ratio Test - correct answer Series Type: All
When to try: With factorials or exponentials

Series Expansion: 1/(1-x) - correct answer

Series Expansion: e^x - correct answer

Series Expansion: Sin(x) - correct answer

Series Expansion: Cos(x) - correct answer