初一数学,过程写纸上谢谢!
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/22 21:24:37
初一数学,过程写纸上谢谢!
![初一数学,过程写纸上谢谢!](/uploads/image/z/5564799-63-9.jpg?t=%E5%88%9D%E4%B8%80%E6%95%B0%E5%AD%A6%2C%E8%BF%87%E7%A8%8B%E5%86%99%E7%BA%B8%E4%B8%8A%E8%B0%A2%E8%B0%A2%21)
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)+1/31^2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)+1/31^2
=(1-1/2^2)*(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+1/31^2
=(1-1/2^4)*(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+1/31^2
=……(看出来了吗,平方差公式一项项消掉了)
=(1-1/2^32)*2+2^31
=2-1/2^31+2^31
=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)+1/31^2
=(1-1/2^2)*(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+1/31^2
=(1-1/2^4)*(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)+1/31^2
=……(看出来了吗,平方差公式一项项消掉了)
=(1-1/2^32)*2+2^31
=2-1/2^31+2^31
=2