1-1/2-1/4-1/8-.-1/1024=?我知道这一题每次都分一半,最后等于1/1024,

1-1/2-1/4-1/8-.-1/1024=?我知道这一题每次都分一半,最后等于1/1024,
1-1/2-1/4-1/8-.-1/1024=?
我知道这一题每次都分一半,最后等于1/1024,

1-1/2-1/4-1/8-.-1/1024=?我知道这一题每次都分一半,最后等于1/1024,
1-1/2-1/4-1/8-.-1/1024
=1-(1/2+14+1/8+...+1/1024)
=1-(1/2)[1-(1/2)^10]/[1-(1/2)]
=1-1+(1/2)^10
=(1/2)^10
=1/1024

1-1/2-1/4-1/8-......-1/1024
=1/2-1/4-1/8-......-1/1024
=1/4-1/8-......-1/1024
......
=1/512-1/1024
=1/1024

1-1/2-1/4-1/8-......-1/1024=S 两边乘1／2
1/2-1/4-1/8-......-1/1024-1/2048=0.5S
相减
0.5S=1-1+1/2048
S=1/1024

按照等比数列求和公式计算简单多了。【sum＝a*[1-q^n]/(1-q)】
a＝1/2；q＝1/2；n＝10 因为2^10=1024嘛
原式＝=1-1/2*[1-(1/2)^10]/(1-1/2）＝(1/2)^10=1/1024