

A math problem on Glenn Beck - can you solve it? - strategy
http://mindyourdecisions.com/blog/2011/04/01/a-math-problem-on-glenn-beck-can-you-solve-it/

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RiderOfGiraffes
OK, with n growing without bound, and the ratio between n and pi being
transcendental, the value of sin(2n) basically bounces around randomly.

cos(n) is also effectively random, and there's no real relationship between
the sin and cos because everything's "random."

So I'd bet it doesn't converge.

In fact, for any epsilon we can find N such that |sin(2.pi.N)|<epsilon/4. Call
the sum up to that point S - it will not be zero, and then look at the sum up
to 2N. That will be very nearly 2S. Take one step further and the sum will be
roughly 2S+0.7754.

I think that's enough to show it doesn't converge, but I'm typing this between
other tasks and don't have time to be more formal. If anyone really cares then
I'll work on it later.

But no, it doesn't converge.

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uioukyyuk
Hint FAIL. The trick is that it's begging the question, but your spoiler makes
that too obvious... I don't know what convergence is, and RoG's comment was
exactly what I came here to say :)

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RiderOfGiraffes
Seems to me it's non-convergent.

