Convergence Business

Question 1

what do do with things like this: 1/2^n

Answer 1

This is a geometric series, and so converges when the common ratio is less than |1|.

Question 2

How can you know that a series doesn’t converge?

Answer 2

if the n term isn’t approaching 0.

Question 3

Alternating Series test indicates convergence if:

Answer 3

bn ≥ 0, bn decreasing, Lim as n-> ∞ of bn = 0

Question 4

What happens with every power series?

Answer 4

-Symmetric convergence with radius R around the center. -diverges outside radius R. -Always need to check endpoint to find the interval of convergence.