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1/2+1/4+1/8+1/16+1/32+1/64+1/128的简便运算

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 =(1/2+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...

可以这样1-1/2=1/2, 1/2-1/4=1/4, 1/4-1/8=1/8, 1/8-1/16=1/16, 1/16-1/32=1/32, 1/32-1/64=1/64 所以1/2+1/4+1/8+1/16+1/32+1/64=(1-1/2)+(1/2-1/4)+(1/4-1/8)+(1/8-1/16)+(1/16-1/32)+(1/32-1/64)=1-1/64=63/64 或者画出一个圆先二分之一等分...

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可写作1-1/2,1/4可写作1/2-1/4,以此类推。 上式等于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+1/128-1/256+1/256-1/512 中间的数重复加减可相抵消,最后等于1-1/512=511/512 望采纳^_^

算下来是63/64,约等于1

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

假设:s=1/2+1/4+1/8+1/16+1/32+1/64 ;则:2s=1+1/2+1/4+1/16+1/32 ;用2s-s(相同项全部抵消,只剩首位2项) ; s=1-1/64=63/64。 1.分式加减法法则:(1)通分:把异分母的分式化为同分母分式的过程,叫做通分。(2)同分母分式的加减法法则:...

原式=(1/2+1/4)+(1/8+1/16)+(1/32+1/64)+1/128 =(2/4+1/4)+(2/16+1/16)+(2/64+1/64)+1/128 =3/4+3/16+3/64+1/128 =3x(1/4+1/16+1/64)+1/128 =3x(16/64+4/64+1/64)+1/128 =3x(21/64)+1/128 =63/64+1/128 =126/128+1/128 =127/128

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