230问答网 > (3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1

(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1

2024-12-23 03:59:54

推荐回答（3个）

回答1：

(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)+1
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3-1)+1
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)/(3-1)+1
=(3^8-1)(3^8+1)(3^16+1)/(3-1)+1
=(3^16-1)(3^16+1)/(3-1)+1
=(3^32-1)/(3-1)+1
=3^31-1+1
=3^31

回答2：

(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1
=[(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1]/(3-1)
=[(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)+1]/(3-1)
=[(3^4-1)(3^4+1)(3^8+1)(3^16+1)+1]/(3-1)
=[(3^8-1)(3^8+1)(3^16+1)+1]/(3-1)
=[(3^16-1)(3^16+1)+1]/(3-1)
=[(3^32-1)+1]/(3-1)
=3^32/2

回答3：

=（3-1）(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)÷（3-1）+1
=（3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)÷2+1(平方差公式）
=（3^16-1）÷2+1
=3^16/2+1/2