Calc Final Flashcards
(35 cards)
When does the divergence test show convergence?
Never, cannot show divergence
When does the divergence test show divergence?
If lim(a –> infinity) does not equal 0, the series divergences
When does the geometric test show convergence?
When absolute value of r is less than 1
When does the geometric test show divergence?
When absolute value of r is greater than or equal to 1
When does p-series test show convergence?
When p is greater than 1
When does p-series show divergence?
When p is less than or equal to 1
When does integral test show convergence?
When the integral from 1 to infinity of f(x)dx converges
When does integral test show divergence?
When the integral from 1 to infinity of f(x)dx diverges
Condition for integral test to be applied
f(x) has to be positive, continuous, and decreasing for x values equal to or greater than 1
When does direct comparison test show convergence?
When the series is smaller than a known convergent
When does direct comparison test show divergence?
When the series is bigger than a known divergent
What should you try to compare a series to in direct comparison?
P-series or geometric series
When does limit comparison show convergence?
When the lim(n–>infinity) of An/Bn = L > 0 and Bn is known to be convergent
When does limit comparison show convergence?
When the lim(n–>infinity) of An/Bn = L > 0 and Bn is known to be divergent
When is LCT inconclusive?
When L = 0 or L = infinity
When does alternating series test show convergence?
When lim(n–>infinity) of Bn = 0 and Bn+1 is less than or equal to Bn
When does AST show divergence?
Doesn’t say anything about divergence; if the lim(n–>infinity) of the alternating series does not equal 0, use divergence test
When does ratio test show convergence?
When lim(n–>infinity) of the absolute value of An+1 over An = L < 1
When does ratio test show divergence?
When lim(n–>infinity) of the absolute value of An+1 over An = L > 1
When is the ratio test inconclusive?
When L = 1
When is the ratio test helpful?
With factorials and ( )^n
When does root test show convergence?
When lim(n–>infinity) of square root of the absolute value of An = L < 1
When does root test show divergence?
When lim(n–>infinity) of square root of the absolute value of An = L > 1
When is root test inconclusive?
When L = 1
