作业帮简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 13:40:48
简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
简算:(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
你可以先找找规律
2+1=2^1+2^0
(2+1)(2^2+1)=2^3+2^2+2^1+2^0
(2+1)(2^2+1)(2^4+1)=(2^3+2^2+2^1+2^0)(2^4+1)=2^7+……+2^0
所以归纳得到(2+1)(2^2+1)(2^4+1)…(2^32+1)=2^63+……+2^0
所以原式=2^63+……+2^0+1=(1-2^64)/(1-2)+1=2^64
(2+1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^2-1)(2^2+1)(2^4+1)…(2^32+1)+1
=(2^4-1)(2^4+1)…(2^32+1)+1
=......
=(2^32-1)(2^32+1)+1
=2^64