求教(2+1)(22+1)(24+1)(28+1)…(264+1)+1等于多少?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 13:25:31
![求教(2+1)(22+1)(24+1)(28+1)…(264+1)+1等于多少?](/uploads/image/z/375309-45-9.jpg?t=%E6%B1%82%E6%95%99%282%2B1%EF%BC%89%2822%2B1%EF%BC%89%2824%2B1%EF%BC%89%2828%2B1%EF%BC%89%E2%80%A6%28264%2B1%EF%BC%89%2B1%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
求教(2+1)(22+1)(24+1)(28+1)…(264+1)+1等于多少?
求教(2+1)(22+1)(24+1)(28+1)…(264+1)+1等于多少?
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.
原式=(2-1)(2+1)(2^2+1)(2^4+1)( 2^8+1)( 2^16+1)( 2^32+1)( 2^64+1)+1
连续利用平方差公式可得=2^128-1+1=2^128
即
(2+1)(2^2+1)(2^4+1)......(2^64+1) +1
=(2-1)(2+1)(2^2+1)(2^4+1)......(2^64+1) +1
=(2^...
全部展开
原式=(2-1)(2+1)(2^2+1)(2^4+1)( 2^8+1)( 2^16+1)( 2^32+1)( 2^64+1)+1
连续利用平方差公式可得=2^128-1+1=2^128
即
(2+1)(2^2+1)(2^4+1)......(2^64+1) +1
=(2-1)(2+1)(2^2+1)(2^4+1)......(2^64+1) +1
=(2^2-1)(2^2+1)(2^4+1)......(2^64+1) +1
=(2^4-1)(2^4+1)......(2^64+1) +1
=2^128-1 +1
=2^128
收起