Sum(1 / n^p) as n goes from 1 to ∞.
Basically, if p ≤ 1, the series diverges. If p > 1, the series converges.
Notes below.
Tuesday, March 27, 2012
March 26 - p-Series Test
We talked about several things today - the highlights were using an (improper) integral to argue that the series 1 + 1/2 + 1/3 + 1/4 + ... + 1/n + ... diverges and then generalizing to any sum of the form:
Sum(1 / n^p) as n goes from 1 to ∞.
Basically, if p ≤ 1, the series diverges. If p > 1, the series converges.
Notes below.
Sum(1 / n^p) as n goes from 1 to ∞.
Basically, if p ≤ 1, the series diverges. If p > 1, the series converges.
Notes below.
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment