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by ilyagr
4090 days ago
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Another UPDATE: I a cousin comment, Retric proves that the integral of 1/log(x)^2 diverges. The point is that log(n)^2 < n for x > 2 (you can prove this by calculus: the only maximum of the function log(x)^2/x is at x=e). So, 1/log(x)^2 > 1/x, and the integral of 1/x diverges. The most fun way to prove the last statement is that the integral of 1/x from 1 to infinity is greater than 1/2 + 1/3 + 1/4 + 1/5 + ... > 1/2 + 1/4 + 1/4 + 1/8 + ... = 1/2 + 2 * 1/4 + 4 * 1/8 + ... = 1/2 + 1/2 + 1/2 + .... |
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