1 / 3 + 1 / 6 + 1 / 10 + 1 / 15 + 1 / (1 + 2 + 3 + 4 + 5 +... N) =? Find the law

The original formula = 1 / ((1 + 2) * 2 / 2) + 1 / ((1 + 3) * 3 / 2) + 1 / ((1 + 4) * 4 / 2) + +1/((1+n)*n/2)
=2/(2*3)+2/(3*4)+2/(4*5)+2/(5*6)+…… +2/(n*(n+1))
=2(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+…… +1/n-1/(n+1))
=(n-1)/(n+1)

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