1/1×2+1/2×3+1/3×4…+1/n×(n-1)

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1/1×2+1/2×3+1/3×4…+1/n×(n-1)
1/1×2+1/2×3+1/3×4…+1/n×(n-1)

1/1×2+1/2×3+1/3×4…+1/n×(n-1)
原式=1-1/2+1/2-1/3+1/3-1/4+……+1/(n-1)-1/n
=1-1/n
=(n-1)/n

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

=1-1/2+1/2-1/3+1/3-1/4+……+1/(n-1)-1/n
=1-1/n
=(n-1)/n