根据高斯定理解答一道数学难题求1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+100)的值.
问题描述：
根据高斯定理解答一道数学难题
求1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+100)的值.
答
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+100)
=2/(1*2)+2/(2*3)+....2/(100*101)
=2*(1-1/101)
=200/101
答
1+2+3+...+n=n(n+1)/21/(1+2+3+..+n)=2/[n(n+1)]=2[1/n-1/(n+1)]1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+100)=2[1-1/2+1/2-1/3+1/3-.+1/100-1/101]=2*100/101=200/101