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1/2+1/4+1/8+1/16+1/32+1/64+1/128等于?为什么

1/2+1/4+1/8+1/16+1/32+1/64+1/128=127/128 因为每一项后面的分母都是前面的一半,所以你可以在原来的式子最后加1/128,可以发现从后往前算,就是2个1/128加起来变成1个1/64,然后2个1/64加起来变成1个1/32,依次类推,...最后就是2个1/2加起来变成1. ...

1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 =1-1/256 =255/256

1/2+1/4+1/8+1/16+1/32+1/64+1/128 =(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128)-1/128 =(1/2+1/4+1/8+1/16+1/32+1/64+1/64)-1/128 =1-1/128=127/128 每一项后面的分母都是前面的一半,所以可以在原来的式子最后+1/128,可以发现从后往前算,就是2...

可如下简便计算: (1)用等比数列公式计算: Sn=a1(1-q^n)/(1-q) =(1/2)x[1-(1/2)^7]/(1-1/2) =1-(1/2)^7 =1-1/128 =127/128 (2)1/2+1/4+1/8+1/16+1/32+1/64+1/128 =(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128)-1/128 =2x(1/2...

127/128 (1)1/2+1/4+1/8+1/16+1/32+1/64+1/128 =(1-1/2)+(1/2-1/4)+(1/4-1/8)+......+(1/64-1/128) =1-1/2+1/2-1/4+1/4-1/8+......+1/64-1/128 =1-1/128 =127/128 (2)因为每一项后面的分母都是前面的一半,所以你可以在原来的式子最后+1/128,可...

等比数列前n项和公式 1/2+1/4+1/8+1/16+1/32+1/64+1/128 =1/2+(1/2)^2+(1/2)^3+……+(1/2)^7 =1/2×[1-(1/2)^7]/(1-1/2) =1-(1/2)^7 =1-1/128 =127/128

1/2+1/4+1/8+1/16+1/32+1/64+1/128 =1-1/2+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+(1/32-1/64)+(1/64-1/128) =1-1/128 =127/128

1/2+1/4+1/8+1/16+1/32+1/64+1/128 =1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128-1/128 =1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/128 =1/2+1/4+1/8+1/16+1/32+1/32-1/128 =1/2+1/4+1/8+1/16+1/16-1/128 =1/2+1/4+1/8+1/8-1/128 =1/2+1/4+1/4-1/128 =1-1...

1/2+1/4+1/8+1/16+1/32+1/64等于63/64 使用简便计算即可,计算过程如下: 1/2+1/4+1/8+1/16+1/32+1/64 =1/2+1/4+1/8+1/16+1/32+1/64+1/64-1/64 =1/2+1/4+1/8+1/16+1/32+1/32-1/64 =1/2+1/4+1/8+1/16+1/16-1/64 =1/2+1/4+1/8+1/8-1/64 =1/2+1/4+1...

1/128,因为每个数都是前数的一半,所以只要加最后一个数,就可以凑成前一个数,以此类推,得1 也可以用数列公式来解释,太复杂怕你不懂 简单的就是所有数乘以128,相加后的127,加1为128,所以答案是1/128

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