D: HALP GAIZ!

(Sorry if I'm not supposed to post homework here or something.)

My Analysis prof gives hard problems as extra-credit sometimes, and he gave this one during our first class of the semester yesterday.  I can't get anywhere with it. :(  It looks like it should be totally easy, but I'm not seeing it.  I just have to prove that the sequence {sin(1), sin(4), sin(9), ...} doesn't converge. The numbers 1,4,9... are the integer squares.

Anyone have any ideas?

>>4
You can't brute force a convergence test, idiot.

>>5
Well n^2 gets large, so what you wrote would go to minus infinity, so I think maybe you meant something different.


Say the sequence converged to L.  Then L is between -1 and 1, and there are in general two numbers a and b between 0 and 2pi that give sin(x) = L.  So convergence would mean that for large n, the numbers n^2, (n+1)^2,...  are all very close to a or b plus some integer multiple of 2pi.

It seems pretty clear that's impossible, but I can't see how to prove it (yet).