解：原式=6×1/(1×3)+6×1/(2*4)+6×1/(3*5)+...+6×1/n*(n+2)
=6×1/2×(1-1/3)+6×1/2×(1/2-1/4)+6×1/2×(1/3-1/5)+......+6×1/2×[1/n-1/(n+2)]
=3×(1-1/3)+3×(1/2-1/4)+3×(1/3-1/5)+......+3×[1/n-1/(n+2)]
=3×[1-1/3+1/2-1/4+1/3-1/5+......+1/n-1/(n+2)]
=3×[1+1/2-1/(n+1)-1/(n+2)]
=3×n(3n+5)/2(n+1)(n+2)
=3n(3n+5)/2(n+1)(n+2)
1+4+9+……+n^2=n(n+1)(2n+1)/6 3+6+9+……+3n=3n(n+1)/2 两式相加，即得n(n+1)(n+5)/3
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