1-1/2-1/4-1/8-1/16-1/321/2+1/4+1/8+16/11/2+1/6+1/12+1/20+1/301/3+1/15+1/35+1/63
问题描述:
1-1/2-1/4-1/8-1/16-1/32
1/2+1/4+1/8+16/1
1/2+1/6+1/12+1/20+1/30
1/3+1/15+1/35+1/63
答
1-1/2-1/4-1/8-1/16-1/32
=1-(1-1/2)-(1/2-1/4)-(1/4-1/8)-(1/8-1/16)-(1/16-1/32)
=1-1+1/2-1/2+1/4-1/4+1/8-1/8+1/16-1/16+1/32
=1/32
1/2+1/4+1/8+16/1
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+(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+1/6+1/12+1/20+1/30
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6
1/3+1/15+1/35+1/63
=(2/3+2/15+2/35+2/63)÷2
=【(1-/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)】÷2
=【1-1/3+1/3-1/5+1/5-1/7+1/7-1/9】÷2
=【1-1/9】÷2
=(8/9)÷2
=4/9