Apa itu Deret Harmonik?

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Oresme's proof: grouping shows divergence

1 + 1/2 + (1/3+1/4) + (1/5+…+1/8) + …

Each group ≥ 1/2: 1/3+1/4 > 2×1/4 = 1/2 and 1/5+…+1/8 > 4×1/8 = 1/2

We can always add another group ≥ 1/2, so the total grows without bound. QED (Oresme ~1360)

H(n) grows like ln(n) plus γ

H(n) and ln(n) grow together, always differing by approximately γ ≈ 0.5772. Both diverge: to reach H(n) = 100 requires about 10^43 terms.

How absurdly slow: milestones for H(n) exceeding round numbers

~10^43 terms are needed to reach H(n)=100. More than atoms in the observable universe.

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Apa hubungan antara deret harmonik dan gamma?

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