Sequences and Series Flashcards
All known ways to solve them as well as some tricks etc
Complete list (more for admin purposes)
Bounded and monotone, Squeeze, GF
Definition
Partition thingy
Geometric
Cauchy sequence
Subsequences
Defintion
GFT
Bounded below potentially?
Partial sums
Comparison test
Bounded above and positive terms
Absolute convergence
Ratio test
Cauchy condensation
Leibniz
Divergence test
Comparison test thingy
To be added:
Epsilon delta defintiion
New theorem thing (wait for more understanding)
What are the main theorems for sequences?
Bounded and Monotone
Squeeze Theorem
Growth Factor test
What can be a very cute way to show a limit of a sequence?
Guess a limit and use the definition
Methods for a limit of a sequence that need to be proved if used?
Some different subsequences in combination can shpw convergence. Eg even and odd, (any partition?)
Sequences: simple but often forgotten especially when it looks complicated?
Geometric. Iv had trouble with this when i have (2^n)/(3^n)
Final really cool way to prove a sequences converges?
Show its a Cauchy sequence
Advantage - you dont need to know the limit
What are the 4 ways you may know a sequences converges?
Growth Factor test
Subsequences with different limits
Definition
(Possible if bounded below by something that diverges
Explain the primary way to test if a series converges?
Using partial sums. Find an nth term eg by telescoping or show that it is bounded and if all terms are positive (absolute convergence) then bounded and monotone
What are the different theorems you can use to show convergence of a series?
Comparison test
Ratio test
Cauchy condensation
Leibniz alternating series test
What is a good fact to keep in mind when dealing with series?
If it converges absolutely then it converges
What is the quickest way to see if a series diverges?
Divergence test (sequence must tend to 0)
Other way to prove a series diverges?
Convergence test thingy (show its bounded below by a series that tends to infinity)
