简单是数列求和1/1+1/3+1/6+1/10+1/15+.+1/(（n+1)*n/2)=?
问题描述：
简单是数列求和
1/1+1/3+1/6+1/10+1/15+.+1/(（n+1)*n/2)=?
答
1/(（n+1)*n/2)=2/n-2/n+1
1/1+1/3+1/6+1/10+1/15+........+1/(（n+1)*n/2)=2-1+1-2/3+.....+2/n-2/n+1=2-2/n+1=2n/n+1
答
1+1/3+1/6+1/10+1/15+...+1/(（n+1)*n/2)
=2(1/1-1/2)+2(1/2-1/3)+2(1/3-1/4)+2(1/5-1/6)+...+2[1/n-1/(n+1)]
=2(1/1-1/2+1/2-1/3+1/3-1/4+1/5-1/6+...+1/n-1/n+1)
=2(1/1-1/n+1)
=2*n/(n+1)
答
1/[(n+1)n/2]
=2/n(n+1)
=2*[1/n-1/(n+1)]
所以原式=2*[1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)]
=2*[1-1/(n+1)]
=2n/(n+1)
答
1/(（n+1)*n/2)=2*(1/n-1/(n+1))
带入原式=2*(1-1/(n+1))=2n/(n+1)