Question

用裂项相消法解该题！

1/1×3+1/2×4+……+1/98×100
怎么解？急急急！！！

Answer 1

1/n(n+2)=[1/n-1/(n+2)]/2，即1/1×3=(1/1-1/3)/2;1/2×4=(1/2-1/4)/2;......
于是1/1×3+1/2×4+……+1/98×100=1/1-1/3+1/2-1/4+1/3-1/5.....+1/97-1/99+1/98-1/100
=1+1/2-1/99-1/100=(9900+4950-100-99)/9900=14651/9900

追问

谢谢