1/1*4+1/4*7+1/7*10+.+1/52*55*+1/55*58=?
问题描述:
1/1*4+1/4*7+1/7*10+.+1/52*55*+1/55*58=?
答
1/1*4=(1/3)*(1-1/4)
1/4*7=(1/3)*(1/4-1/7)
1/7*10=(1/3)*(1/7-1/10)
1/1*4+1/4*7+1/7*10+.+1/52*55*+1/55*58
=(1/3)*(1-1/4)+(1/3)*(1/4-1/7)+(1/3)*(1/7-1/10)+……+(1/3)*(1/55-1/58)
=(1/3)*(1-1/4+1/4-1/7+1/7-1/10+1/10-……-1/55+1/55-1/58)
=(1/3)*(1-1/58)
=(1/3)*(57/58)
=19/58