（1） 1/(1×2） + 1/(2×3) + 1/(3×4)+……+ 1/(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
(2) 1 + 1/(1+2) + 1/(1+2+3) + ……+ 1/(1+2+3 +4 +……+n)
= 1 + 1[(1/2)(1+2)2] + 1/[(1/2)(1+3)*3] + ……+1/[(1/2)n(n+1)]
= 1 + 2[1/(2*3) + 1/(3*4) +……+ 1/n*(n+1)]
= 1 + 2[ 1/2 - 1/3 + 1/3 - 1/4 + ……+1/n - 1/(n+1) ]
= 1 + 2[ 1/2 - 1/(n+1)]
= 1 + 2(n-1)/2(n+1)
= 1 + (n-1)/(n+1)
= 2n/(n+1)