Calc 2 Exam 3 Flashcards
What is the difference between series and sequences?
Series is adding up all the terms in a sequence, while a sequence is not added together.
Geometric Series
a + ar + ar^2 + ar^3….. + ar^n
Or the sum of ar^(n-1) in which a is the first terms and r is what each term is multiplied by.
-series converges if r
Telescoping Series
Once you start adding the series, they values begin to cancel out. The terms can then be taken the limit of to find the final number the series converges to.
-split up series if need be
Limit Test
If the limit of a(n) does not equal 0 then the series diverges. This does not test convergence because if the limit does equal 0, it can still diverge.
Integral Test
If the function is decreasing, continuous, and positive then integrating the function from 1to infinity and the answer is not 0 or infinity then it is convergent. Otherwise it diverges.
P-Series Test
Finding the sum of 1/n^p and…
- p > 1 then it converges
- p
Limit Comparison Test
If you take the limit of an/bn and the answer = c > 0 or finite, then either both series converge or diverge
What is the s(n) equal to?
The sum of all a(n) sequences
Alternating Series Test
The sum of (-1)^(n-1) satisfies…..
a) b(n+1)
Absolutely Convergent
If the series in absolute value is also convergent.
Conditionally Convergent
If the series is convergent but the absolute value series is divergent.
Ratio Test
a) if the limit of [a(n+1)/an] = L 1 then series diverges
c) if the limit of [a(n+1)/an] = L = 1 then series is inconclusive
Root Test
a) if the limit of (n)root (an) = L 1 then series is divergent
c) if the limit of (n)root (an) = L = 1 then series is inconclusive
Power Series
Sum of cn(x-a)^n
How to find where a series converges with a power series…
Take the ratio test
