AnteCantelope
Registered User regular

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.

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.

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## Posts

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

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RedDeliciousonCool, 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.)

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