计算:1+(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)-?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 15:53:55
![计算:1+(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)-?](/uploads/image/z/14990002-34-2.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A1%EF%BC%8B%281%2B2%29%281%2B2%5E2%29%281%2B2%5E4%29%29%281%2B2%5E8%29%26%238943%3B%26%238943%3B%281%2B2%5E256%29-%3F)
计算:1+(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)-?
计算:1+(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)-?
计算:1+(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)-?
1+(1+2)(1+2^2)(1+2^4)(1+2^8)⋯⋯(1+2^256)
=1+(2-1)(1+2)(1+2^2)(1+2^4)(1+2^8)⋯⋯(1+2^256)
=1+(2^2-1)(1+2^2)(1+2^4)(1+2^8)⋯⋯(1+2^256)
=1+(2^4-)(1+2^4)(1+2^8)⋯⋯(1+2^256)
=1+(2^8-))(1+2^8)⋯⋯(1+2^256)
=1+(2^8-1)⋯⋯(1+2^256)
………………………………………………
=1+2^512-1
=2^512
1+(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)
=1+(2-1)(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)
=1+(2^2-1)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)
=……
=1+2^512-1
=2^512
1+(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)
=1+(2-1)(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256) 利用平方差公式
=2^512-1+1
=2^512能详细一点吗?=1+(2-1)(1+2)(1+2^2)(1+2^4))(1+2^8)⋯...
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1+(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256)
=1+(2-1)(1+2)(1+2^2)(1+2^4))(1+2^8)⋯⋯(1+2^256) 利用平方差公式
=2^512-1+1
=2^512
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