小学六年级数学题求解!~~1024+512+256+.2+1+1/2+1/4+1/8+.1/512+1/1024等于多少?请写出简便算式.

Question

小学六年级数学题求解!~~
1024+512+256+.2+1+1/2+1/4+1/8+.1/512+1/1024等于多少?请写出简便算式.

Answer 1

设1024+512+256+.2+1+1/2+1/4+1/8+.1/512+1/1024=x
2（512+256+.2+1+1/2+1/4+1/8+.1/512+1/1024+1/2048)=x
2(1024+512+256+...2+1+1/2+1/4+1/8+.1/512+1/1024+1/2048-1024)=x
2(x+1/2048-1024)=x
2x+1/1024-2048=x
x=2048-1/1024
所以
1024+512+256+.2+1+1/2+1/4+1/8+.1/512+1/1024=2048-1/1024.