求一小学分数巧算题,

题目

求一小学分数巧算题,
是一分数,分子为1/2-1/4+1/6-1/8+1/10………………+1/198-1/200
分母为1/51+1/52+1/53+………………1/100

答案

1/2-1/4+1/6-1/8+1/10-1/12+…+1/198-1/200
=(1-1/2+1/3-1/4+ ...+1/99-1/100)/2
=[(1+1/2+ ...+1/99+1/100)-2(1/2+1/4+ ...+1/98+1/100)]/2
=[(1+1/2+ ...+1/99+1/100)-(1+1/2+ ...+1/49+1/50)]/2
=(1/51+1/52+1/53+ ...+1/99+1/100)/2
所以原式
=(1/2)(1/51+1/52+1/53+ ...+1/99+1/100)/(1/51+1/52+1/53+…+1/100)
=1/2