3/4+3/16+3/63+3/256
=1-1/4+(1/4)×(3/4)+(1/4)×(1/4)×(3/4)+(1/4)×(1/4)×(1/4)×(3/4)
=1-(1/4)(1-3/4)+(1/4)×(1/4)×(3/4)+(1/4)×(1/4)×(1/4)×(3/4)
=1-(1/4)×(1/4)+(1/4)×(1/4)×(3/4)+(1/4)×(1/4)×(1/4)×(3/4)
=1-(1/4)×(1/4)×(1-3/4)+(1/4)×(1/4)×(1/4)×(3/4)
=1-(1/4)×(1/4)×(1/4)+(1/4)×(1/4)×(1/4)×(3/4)
=1-(1/4)×(1/4)×(1/4)×(1-3/4)=1-(1/4)×(1/4)×(1/4)×(1/4)=1-1/256=255/256
过程是不是很麻烦.基本思路是将3/4分解成1-1/4,再提取公因式,化简计算.