math

prove that 1+1/4+.........+1/n^2<2-1/n

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  1. true for k=1?
    1/1^2 < 2 - 1/1 ?
    no. well, maybe
    1 + 1/2^2 < 2 - 1/2 ?
    5/4 < 3/2 ?
    yes. So, we'll do induction for k>2
    assume
    ∑ 1/k^2 < 2 - 1/k
    now show that
    ∑ 1/k^2 + 1/(k+1)^2 = 2 - 1/k + 1/(k+1)^2 < 2 - 1/(k+1)^2
    see what you can do with that.
    I bet google can help if you still get stuck.

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