4/5*7+4/7*9+4/9*11+.+4/53*55

问题描述:

4/5*7+4/7*9+4/9*11+.+4/53*55

4/(5×7)+4/(7×9)+4/(9×11)+....+4/(53×55)
=(1/5-1/7)×2+(1/7-1/9)×2+(1/9-1/11)×2+......+(1/53-1/55)×2
=(1/5-1/7+1/7-1/9+1/9-1/11+.....-1/53+1/53-1/55)×2
=(1/5-1/55)×2
=(2/11)×2
=4/11

4/5*7+4/7*9+4/9*11+.+4/53*55
=2*(2/5*7+2/7*9+2/9*11+...+2/53*55)
=2*(1/5-1/7+1/7-1/9+...+1/53-1/55)
=2*(1/5-1/55)
=2*10/55
=4/11