数学题1/4x1/5x1/6+1/5x1/6x1/7+1/6x1/7x1/8+.+1/98×1/99×1/100=?

数学题1/4x1/5x1/6+1/5x1/6x1/7+1/6x1/7x1/8+.+1/98×1/99×1/100=?
数学题1/4x1/5x1/6+1/5x1/6x1/7+1/6x1/7x1/8+.+1/98×1/99×1/100=?

数学题1/4x1/5x1/6+1/5x1/6x1/7+1/6x1/7x1/8+.+1/98×1/99×1/100=?
由于 1/n(n+1)=1/n-1/(n+1)
原题的通项：
an=1/n(n+1)(n+2)
=[1/n-1/(n+1)]*1/(n+2)
=1/n(n+2)-1/(n+1)*1/(n+2)
=1/2*(1/n-1/(n+2))-[1/(n+1)-1/(n+2)]
逐项相加后消去中间项,你自己可以检验一下,最后得到
1/4*5*6+1/5*6*7+1/6*7*8+.+1/98*99*100
=1/2*{1/4*5-1/99*100}
=247/9900