Good resource for Uni-level maths? Specifically sequences and series

AnteCantelope

I'm doing a first-year maths subject at uni, and while I'm generally OK with it I'm struggling at the moment with sequences, and the lecturer is being not very helpful. Does anyone know a good site that would help me with questions like:
For a series Un = n * Sin(1/n), prove that Un is monotonically increasing and find the value it converges to.

(I'm not just asking you to solve that one for me, because I have a stack of similar ones to go)

Basically I can plot it as a function, and I can brute force an answer that says it converges to 1, but that won't help because the marks are all awarded for proving things, rather than just answering them.

One technique we're meant to use to prove increasing or decreasing is
(Un+1)/(Un) = whatever, and then prove that that's either greater or less than 1, but that doesn't do much for me when Sin is involved.

L|ama

you can probably use that as n approaches infinity sin(1/n) approaches 0, or rather that sin(1/n+1)<sin(1/n) (for integer n of course)

khan academy is generally pretty good but seems to be lacking on sequences and series, MIT's opencourseware is really good too

RedDelicious

See if your textbook can be found on hotmath.com

AnteCantelope

L|ama wrote: »

you can probably use that as n approaches infinity sin(1/n) approaches 0, or rather that sin(1/n+1)<sin(1/n) (for integer n of course)

khan academy is generally pretty good but seems to be lacking on sequences and series, MIT's opencourseware is really good too

Cool, there seems to be a lot of detail on there, I'll have a better look later.
(sin(1/n) -> 0, but n -> infinity, so n*sin(1/n) is less simple.)

L|ama

yyyyeah my first instinct would be to go for the fact that sinx~=x for small x so sin(1/n)~=1/n, but that doesn't really give you a precise value of what happens (although it does actually work out in this case and the limit is 1, according to wolframalpha)