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(1|8+1|24+1|48+1|80+1|120+1|168+1|224)*64
题目详情
(1|8+1|24+1|48+1|80+1|120+1|168+1|224)*64
▼优质解答
答案和解析
(1/8+1/24+1/48+1/80+1/120+1/168+1/224)*64
=(1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16)*64
=[1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+1/2*(1/81/10)+1/2*(1/10-1/12)+1/2*(1/12-1/14)+1/2*(1/14-1/16)]*64
=1/2*[1/2-1/4+1/4-1/6+1/6-1/8+1/81/10+1/10-1/12+1/12-1/14+1/14-1/16]*64
=32*[1/2-1/16]
=32*1/2-32*1/16
=16-2
=14
=(1/2*4+1/4*6+1/6*8+1/8*10+1/10*12+1/12*14+1/14*16)*64
=[1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+1/2*(1/81/10)+1/2*(1/10-1/12)+1/2*(1/12-1/14)+1/2*(1/14-1/16)]*64
=1/2*[1/2-1/4+1/4-1/6+1/6-1/8+1/81/10+1/10-1/12+1/12-1/14+1/14-1/16]*64
=32*[1/2-1/16]
=32*1/2-32*1/16
=16-2
=14
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