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Problem

H_$n$ = 1 + 1/2 + 1/3 + ... + 1/$n$ is defined as the $n$th Harmonic number.

1. Prove that H_$n$ ln($n$) + 1/(2$n$) + $k$, where 0.5 $k$ 1.
2. By using $k$ = 0.5772, estimate the sum of the first one hundred Harmonic numbers.