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
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
