计算（1+1/2;）*（1+1/2²)*(1+1/2四次方）*（1+1/2八次方）+1/2十五次方

题目

计算（1+1/2;）*（1+1/2²)*(1+1/2四次方）*（1+1/2八次方）+1/2十五次方

答案

（1+1/2;）*（1+1/2²)*(1+1/2四次方）*（1+1/2八次方）+1/2十五次方
=2*(1-1/2)[（1+1/2;）*（1+1/2^2;)*(1+1/2^4）*（1+1/2^8）]+1/2^15
=2*(1-1/2^2)(1+1/2^2;)*(1+1/2^4）*（1+1/2^8）+1/2^15
=2*(1-1/2^4)(1+1/2^4）*（1+1/2^8）+1/2^15
=2*(1-1/2^8)(1+1/2^8）+1/2^15
=2*(1-1/2^16)+1/2^15
=2-1/2^15+1/2^15
=2