1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+.+100)
=1/1+1/(2*(2+1)/2)+...+1/(n*(n+1)/2)
=1/1+2(1/2-1/3+1/3-1/4+.+1/n-1/(n+1))
=1+2(1/2-1/(n+1))
=2-2/(n+1)
原式为n=100时的数值
即原式=2-2/101=200/101