Question

请教一道数学题，急！！！ 原题是这样的 1/1*2*3+1/2*3*4+......+1/98*99*100

Answer 1

1/n(n+1)(n+2)
=(1/n-1/(n+1))*1/(n+2)
=1/n*1/(n+2)-1/(n+1)*1/(n+2)
=1/2*(1/n-1/(n+2))-1/(n+1)+1/(n+2)

1/1*2*3+1/2*3*4+......+1/98*99*100
=1/2*(1/1-1/3)-1/2+1/3 +1/2*(1/2-1/4)-1/3+1/4 +1/2*(1/3-1/5)-1/4+1/5 +……+1/2*(1/98-1/100)-1/99+1/100
=0.5*(1-1/3)-1/2+0.5*(1/2-1/4)+0.5*(1/3-1/5)+……+0.5*(1/98-1/100)
=-1/2+0.5*(1+1/2+1/3+1/4+1/5……+1/98-1/3-1/4-1/5-1/6-……-1/100)
=-1/2+0.5*(1+1/2-1/99-1/100)
=……
=4751/19800
过程稍微有点复杂，希望你看得明白~~

Answer 2

1/1*2+1/2*3+1/3*4+......+1/98*99+1/99*100
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+...+1/98-1/99+1/99-1/100
=1-1/100
=99/100

Answer 3

99、100