Question

数学<<0.5+0.25+0.125+.....+1\1024>>怎样做

解决数学问题＜＜0.5+0.25+0.125．．．．+0.0009766＞＞要怎样做

Answer 1

0.5+0.25+0.125+.....+1/1024
=1/2+1/4+1/8+......+1/1024
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+......+(1/512-1/1024)
=1-1/2+1/2-1/4+1/4-1/8+......+1/512-1/1024
=1-1/1024
=1023/1024
答案就是1023/1024，是根据小数化成分数来做的，
因为化成分数比用小数方便

Answer 2

1/2+1/4+1/8+1/16+……+1/1024

这种题目共有三种做法：

1、通分，显然有些麻烦

2、1楼的裂项

3、补一个最后的分数1/1024，同时在减去一个1/1024

2楼的忘了减去1/1024

Answer 3

补上1/1024:
=0.5+…………+1/512+1/1024+1/1024
=0.5+…………+1/128+1/512+1/512
=0.5+…………+1/128+1/128
…………
=1
所以原式=1-1/1024=1023/1024

Answer 4

0.5+0.25+0.125+.....+1/1024
=1/2+1/4+1/8+......+1/1024
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+......+(1/512-1/1024)
=1-1/2+1/2-1/4+1/4-1/8+......+1/512-1/1024
=1-1/1024
=1023/1024