作业帮简便计算1/2+1/4+1/8+1/16+.+1/128+1/256
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简便计算1/2+1/4+1/8+1/16+.+1/128+1/256
简便计算1/2+1/4+1/8+1/16+.+1/128+1/256
简便计算1/2+1/4+1/8+1/16+.+1/128+1/256
S=1/2+1/4+1/8+1/16+.+1/128+1/256
2S=1+1/2+1/4+1/8+1/16+.+1/128
S=2S-S
=1-1/256
=255/256
1/2+1/4+1/8+1/16+......+1/128+1/256
=1-1/256
=255/256
S=1/2+1/4+1/8+1/16+......+1/128+1/256 (1)
(1/2)S =1/4+1/8+1/16+......+1/128+1/256 +1/512 (2)
(1)-(2)
(1/2)S = 1/2 - 1/512
S = 510/512
这就是等比数列求和，直接带入公式，这个题目中a1=1/2,q=1/2,an=1/256那么求和S=(a1-an*q)/(1-q)=255/256.
设S=1/2+1/4+1/8+1/16
2S=2*(1/2+1/4+1/8+1/16)=1+1/2+1/4+1/8
2S-S=[1+(1/2+1/4+1/8)]-[(1/2+1/4+1/8)+1/16]=1-1/16=15/16
以此类推
1/2+1/4+1/8+1/16+......+1/128+1/256=1-1/256 =255/256
1/2+1/4+1/8+1/16+......+1/128+1/256
=1-1/256
=255/256
=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+……+1/64-1/128+1/128-1/256=1-1/256=255/256