Summation of arithmetic sequence 1/1+1/(1+2)+1/(1+2+3).+1/(1+2+3+..N)

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

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