怎样用转化或替换的策略计算这几道算式?

题目

怎样用转化或替换的策略计算这几道算式?
1/2+1/4+1/8+1/16 1/2+1/3+1/6+1/12 1/3+1/5+1/15

答案

1/2+1/4+1/8+1/16
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)
=1-1/16
=15/16
1/2+1/3+1/6+1/12
=1/(1*2)+1/3+1/(2*3)+1/12
=(1/1-1/2)+1/3+(1/2-1/3)+1/12
=1+1/12
=13/12
1/3+1/5+1/15
=1/2*[2/3+2/5+2/(3*5)]
=1/2*[2/3+2/5+(1/3-1/5)]
=1/2*[1+1/5]
=1/2*6/5
=3/5
1/3+1/5+1/15
=1/3+1/5+1-14/15
=1/3+1/5+1-7*2/15
=1/3+1/5+1-7*(1/3-1/5)
=1/3+1/5+1-7/3+7/5
=1+8/5-6/3
=8/5-1
=3/5