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阿Q吧 > 1⼀2+3⼀4+7⼀8+15⼀16+31⼀32+63⼀64+127⼀128+255⼀256+511⼀512+1024⼀1023=多少 ·写出简便方法·

1⼀2+3⼀4+7⼀8+15⼀16+31⼀32+63⼀64+127⼀128+255⼀256+511⼀512+1024⼀1023=多少 ·写出简便方法·

2024-11-14 20:50:47

推荐回答（2个）

回答1：

每一项可分解为（2的n次-1）/2的n次=1-1/2的n次 n=1，2.....10共十项然后合在一起算就行了。原式=10-（）括号内的计算方法：分子分母同时乘以2的（n-1）次项，使得分母全部变为2的10此方然后进行计算得到1023/1024
最后
原式=10-1023/1024=9又1/1024

回答2：

设
a＝1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
b＝1/2+1/4+1/8+1/16+ 1/32+ 1/64+ 1/128+ 1/256
那么a+b＝8
b+1/256＝1/2+1/4+1/8+1/16+ 1/32+ 1/64+ 1/128+ （1/256+1/256）
＝1/2+1/4+1/8+1/16+ 1/32+ 1/64+（ 1/128+ 1/128）
＝1/2+1/4+1/8+1/16+ 1/32+ （1/64+ 1/64）
＝……
=1
所以b＝1-1/256
a＝8-b＝8-（1-1/256）
＝7+1/256

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