求1/1+1/(1+2)+1/(1+2+3)+.+1/(1+2+3+...n)之和
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求1/1+1/(1+2)+1/(1+2+3)+.+1/(1+2+3+...n)之和求1/1+1/(1+2)+1/(1+2+3)+.+1/(1+2+3+...n)之和求1/1+1/(1+2)+1/(1+
求1/1+1/(1+2)+1/(1+2+3)+.+1/(1+2+3+...n)之和
求1/1+1/(1+2)+1/(1+2+3)+.+1/(1+2+3+...n)之和
求1/1+1/(1+2)+1/(1+2+3)+.+1/(1+2+3+...n)之和
1/1 + 1/(1+2) + 1/(1 + 2 + 3) + …… 1/(1 + 2 + 3+ ……+n)
= 2/1×2 + 2/2×3 + 2/3×4 + …… +2/n×(n-1)
= 2( 1/1×2 + 1/2×3 + 1/3×4 + …… + 1/n×(n-1)
= 2( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ……+ 1/(n - 1) - 1/n
= 2( 1 - 1/n)
= 2( n/n - 1/n)
= 2(n-1)/n