Question

利用平方公差公式计算(2+1)(2^2+1)(2^4+1)(2^8+1)+1

利用平方公差公式计算(2+1)(2^2+1)(2^4+1)(2^8+1)+1

Answer 1

构造平方公差公式
(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=( 2^16-1)+1
=2^16

这种构造方式在数学证明过程中,是常用到的.有时乘上去的式子不是"1",你可以在构造后除以这个式子即可!!!

Answer 2

构造平方公差公式
(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=( 2^16-1)+1
=2^16

Answer 3

在左边乘以(2-1)
那么式子=2^9-1+1=2^9=512

Answer 4

(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=2^16-1+1
=2^16

Answer 5

=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1
=(2^4-1)(2^4+1)(2^8+1)+1
=(2^8-1)(2^8+1)+1
=2^16
=65536