Test 3 Flashcards
What is the form of a geometric series?
ar^n
What value of r does a geometric series converge on?
-1 < r < 1
What is the formula for the sum of a geometric series
(a)/1-r
What does the divergence test tell us?
If the limit n goes to infinity of the series does not go to zero, then it’s divergent. If it the limit does = 0, then inconclusive.
How to find the “a” in a geometric series?
It’s the first term
What is are the conditions for the integral test?
Continuous, decreasing and positive
What is the integral test?
The limit b to infinity of the integral from 1 to b of the the series (as a function) will tell if series converges or not.
What is the form of a p series?
1/n^p
Ex: 1/n^5
What value of p does a p series converge
p > 1
What value of p does a p series diverge?
p <= 1
What is the comparison test?
You compare your series (a) to a different series (b). If series (b) is convergent and greater than series (a), then series (a) is convergent as well. If series (b) is divergent and less than series (a), series (a) is divergent as well. Otherwise inconclusive.
What is the limit comparison and the condition?
The condition is positive terms. If lim n goes to infinity of series (a) / series (b) exists (not including 0) both either converge or diverge depending on the convergence of series (b)
What is the Alternating Series Test?
If your alternating series is decreasing (not including the negative sign) for all n and lim n goes to infinity of your series (do this by covering up the (-1)^n) equals 0, then your alternating series is convergent.
What is absolute convergence?
If the absolute value of your series is convergent, then your original series is convergent as well.
What is conditionally convergent?
If the absolute value of your series is divergent and your original series is convergent, then it’s conditionally convergent.
