2007-10-11

Today's nonsense - Trying to remember the Seinfeld references yesterday (Seven, Soda, ...)
- Spiller in New York with Mrs. Spiller, the mother-in-law, Brandon, and something about Danny Phantom being taken off the air.
- "Who took a bite out of my muffin? Where's the rest of my muffin?" - Ketteman's Seinfeld reference.
- Alyssa's absence, and is now has a truancy

Homework due: comparing improper integrals. Homework due Monday on Spiller's teacher website.

Sequences

Sequences talk about the individual terms. The series is the sum of all the terms of the sequence. Sequences can diverge and converge, just as well as series.

Sequences that have limits as n->infinity converge.
Sequences that do not have limit as n->infinity diverge.

Ex) Determine the convergence or divergence of the sequence with the given n^th term. If the ... if it's false, give a reason why it's false, so if the sequence converges, find its limit.

a_n = (n) / (1-2n) ---------> converges to -0.5

a_{_n} = 3+(-1)^ⁿ ---> diverges because it keeps flipping positive and negative there.

d/dx of a^u = a^u * lna * u'

a_{_n} = (n^{^2}) / (2^{^n}(ln2)^{^2})

a_{_n} = (1+(1/n))^{^n}

Take the natural logarithm of each side.

A number close to 1 that is raised to infinity, approaches e??

What's the ratio test?

e) a_{_n} = (-1)^{^n} (1/n!)
f) a_{_n} = (n+1)/n
g) a_{_n} = (-1)^{^n} (n/(n+1))
h) a_{_n} = ( 3n^{^2} - n + 4 ) / (2n^{^2} + 1)