Calculus

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Is sum of sin(pi/n) DV or CV?
I don't understand why it is DV.

  • Calculus -

    sin pi/1 = 0
    sin pi/2 = 1
    sin pi/3 = .866
    sin pi/4 = .707 and pi/4 = .785
    sin pi/5 = .587 and pi/5 = .628
    .
    .
    .
    sin pi/100 = .0314107 and pi/100 = .0314159
    as we know sin x ---> x as x gets big
    so terms get progressively smaller like 1/n (which converges to e) so I think it converges.

  • WRONG!!! -

    1/n! converges to e
    1/n does not converge!!!!
    every term in our series sin (pi/n) is bigger than 1/n
    So it does NOT converge!!
    (This is what I get for counting on my aged memory)

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