急·····(1+1/2)(1+1/2)^2(1+1/2)^4(1+1/2)^8(1+1/2)^16+(1/2)^31具体过程····
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 19:18:20
![急·····(1+1/2)(1+1/2)^2(1+1/2)^4(1+1/2)^8(1+1/2)^16+(1/2)^31具体过程····](/uploads/image/z/595641-57-1.jpg?t=%E6%80%A5%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%EF%BC%881%2B1%2F2%EF%BC%89%EF%BC%881%2B1%2F2%29%5E2%EF%BC%881%2B1%2F2%EF%BC%89%5E4%EF%BC%881%2B1%2F2%EF%BC%89%5E8%EF%BC%881%2B1%2F2%EF%BC%89%5E16%2B%EF%BC%881%2F2%EF%BC%89%5E31%E5%85%B7%E4%BD%93%E8%BF%87%E7%A8%8B%C2%B7%C2%B7%C2%B7%C2%B7)
急·····(1+1/2)(1+1/2)^2(1+1/2)^4(1+1/2)^8(1+1/2)^16+(1/2)^31具体过程····
急·····
(1+1/2)(1+1/2)^2(1+1/2)^4(1+1/2)^8(1+1/2)^16+(1/2)^31
具体过程····
急·····(1+1/2)(1+1/2)^2(1+1/2)^4(1+1/2)^8(1+1/2)^16+(1/2)^31具体过程····
如果题目没有错误的话
(1+1/2)(1+1/2)^2(1+1/2)^4(1+1/2)^8(1+1/2)^16+(1/2)^31
=(1+1/2)^(1+2+4+8+16)+(1/2)^31
=(1+1/2)^31+(1/2)^31
=(3/2)^31+(1/2)^31
=(3×1/2)^31+(1/2)^31
=3^31×(1/2)^31+(1/2)^31
=(1/2)^31(3^31+1)
如果题目是这样的话
(1+1/2)(1+1/2)^2(1+1/2)^4(1+1/2)^8(1+1/2)^16(1/2)^31
=(1+1/2)^31(1/2)^31
=(3/2)^31(1/2)^31
=(3/4)^31
如果乘方在括号里面时,楼上的回答好像也有问题,下面好像应该为:
=(1-1/2^8)(1+1/2^8)(1+1/2^16)/(1-1/2) (看出来了吗,平方差公式一项项消掉了)
=(1-1/2^16)*(1+1/2^16)/(1-1/2)
=(1-1/2^32)/(1-1/2)
=(1-1/2^32)/(1/2)
=2(1-1/2^32)
=2-(1/2)^31
啊 好长呀
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)这个式子左边乘以再除以(1-1/2)
则式子变为(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)
=(1-1/2^2)*(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)
...
全部展开
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)这个式子左边乘以再除以(1-1/2)
则式子变为(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)
=(1-1/2^2)*(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)
=(1-1/2^4)*(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)
=(1-1/2^8)(1+1/2^8)(1+1/2^16)/(1-1/2) (看出来了吗,平方差公式一项项消掉了)
=(1-1/2^16)*(1+1/2^16)/(1-1/2)
=(1-1/2^32)*2+2^31
=2-1/2^16+2^31
收起