How much is (1 + 1 / 2) + (1 + 2 + 1 / 3) + (1 + 2 + 3 + 1 / 4) +... + (1 + 2 +... + 1 / 99)? You can use Gaussian algorithm, but I don't know how to do it,

1+2+3+…… +n=n(n+1)/21/(1+2+3+…… +n) = 2 / [n (n + 1)] = 2 [1 / N - 1 / (n + 1)] so 1 / (1 + 2) + 1 / (1 + 2 + 3) + +1/(1+2+…… 99)=2[1/2-1/3+1/3-1/4+…… +1/99-1/100]=2(1/2 -1/100)=2(49/100)=49/50

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