Infinite Series Flashcards
Bounded Monotonic Sequence theorem
If a sequence an is bounded and monotonic, then it converges
What is the formula for the sum of a geometric series?
What is the nth term test for divergence?
Write the formula for the Integral Test.
What is the formula for the Limit Comparison Test?
What is the alternating series test?
What is the Alternating Series Remainder test?
How do we approximate the number of terms required given an error?
an+1 < error
What are the definitions of absolute and conditional convergence?
Rearrangement of Series
Guidelines for testing series
What are the 10 strategies to use for testing series?
nth term test, geometric series, telescoping series, p-series, alternating series, integral test, root test, ratio test, direct comparison test, limit comparison test
What are the definitions of nth Taylor and Maclaurin polynomials?
What is Taylor’s Theorem?
What is the definition of a power series?
What’s the definition of a Taylor/Maclaurin series?
Write a power series representation for sinx.
Write a power series representation for cosx.
Write a power series representation for ex.
Write a power series representation for 1/1-x.
Write a power series representation for arctanx.
Write a power series representation for lnx.
Write a power series representation for ax/(1-x)^2.
