作业帮求教(2+1）(22+1）(24+1）(28+1）…(264+1）+1等于多少?
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/13 02:23:39
求教(2+1）(22+1）(24+1）(28+1）…(264+1）+1等于多少?
(2+1)(2^2+1)(2^4+1)(2^8+1）…(2^64+1)+1
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1）…(2^64+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1）…(2^64+1)+1
=(2^4-1)(2^4+1)(2^8+1）…(2^64+1)+1
=(2^8-1)(2^8+1）…(2^64+1)+1
=(2^16-1).(2^64+1)+1
.
=(2^64-1)(2^64+1)+1
=2^128-1+1
=2^128
PS：2^2表示2的2次方,.2^128表示2的128次方.
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1）…(2^64+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1）…(2^64+1)+1
=(2^4-1)(2^4+1)(2^8+1）…(2^64+1)+1
=(2^8-1)(2^8+1）…(2^64+1)+1
=(2^16-1).(2^64+1)+1
.
=(2^64-1)(2^64+1)+1
=2^128-1+1
=2^128
PS：2^2表示2的2次方,.2^128表示2的128次方.