1. （2+1）（2^2+1）（2^4+1）（2^8+1)...（2^64+1） =1 *（2+1）（2^2+1）（2^4+1）（2^8+1）...（2^64+1） =(2-1)*（2+1）（2^2+1）（2^4+1）（2^8+1）...（2^64+1） =... =(2^64-1)(2^64+1) =2^128-1 2.(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8) =[(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)]/[1/2] =... =[(1-1/2^8)(1+1/2^8)]/[1/2] =[1-1/2^16]/[1/2] =2[1-1/2^16] =2-1/2^15

（1）求（2+1）（2^2+1）（2^4+1）（2^8+1）...（2^64+1）的值; 因为2+1=2^2-1=3,所以： （2+1）（2^2+1）（2^4+1）（2^8+1）...（2^64+1） =（2^2-1)*(2^2+1)*(2^4+1).....(2^64+1) =(2^4-1)*(2^4+1)....(2^64+1) =.... =2^(64*2)-1 =2^128-1 (2)求(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)的值 因为：1+1/2=3/2=3*（1/2）=3*(1-1/2),所以： (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8) =3*（1-1/2）*(1+1/2)*（1+1/2^2)*(1+1/2^4)*(1+1/2^8) =3*(1-1/2^2)*(1+1/2^2)*(1+1/2^4)*(1+1/2^8) =3*(1-1/2^4)*(1+1/2^4)*(1+1/2^8) =... =3*(1-1/2^16)