作业帮过程希望用纸写出来,计算(2+1)(2^2+1)(2^4+1)(2^8+1计算(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1.
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 11:16:57
过程希望用纸写出来,计算(2+1)(2^2+1)(2^4+1)(2^8+1计算(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1.
过程希望用纸写出来,计算(2+1)(2^2+1)(2^4+1)(2^8+1
计算(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1.
过程希望用纸写出来,计算(2+1)(2^2+1)(2^4+1)(2^8+1计算(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1.
【答案】2^128
【解析】
思路：在原式乘上（2-1），不断的产生平方差，可以巧解。
(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
原式=(2-1)(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(...
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思路：在原式乘上（2-1），不断的产生平方差，可以巧解。
(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
原式=(2-1)(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^16-1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^32-1)(2^32+1)(2^64+1)+1
=(2^64-1)(2^64+1)+1
=2^128-1+1
=2^128
收起
(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=1*(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2-1)*(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=……
=2^128-1+1
=2^128