题目抄得比较乱,前面的分数都写反了.
应该是：5/6 -7/12 +9/20 -11/30+...+(18+19)/(18×19)-(19+20)/(19×20)
5/6 -7/12 +9/20 -11/30+...+(18+19)/(18×19)-(19+20)/(19×20)
=(2+3)/(2×3)-(3+4)/(3×4)+(4+5)/(4×5)-(5+6)/(5×6)+...+(18+19)/(18×19)-(19+20)/(19×20)
=(1/2+1/3)-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+...+(1/18+1/19)-(1/19+1/20)
=(1/2+1/3+1/4+1/5+...+1/18+1/19)-(1/3+1/4+1/5+1/6+...+1/19+1/20)
=1/2 -1/20
=9/20
很简单,化为分子相同,分母小的,分数的值就大.
变形：
30/7830/8530/6930/66
30/66>30/69>30/78>30/85,因此：
15/33>10/23>5/13>6/17