用平方差公式计算:(²=平方、&sup4;=4次方)
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用平方差公式计算:(²=平方、&sup4;=4次方)
①2(3+1)(3²+1)(3&sup4;+1)(3&sup8;+1)+1
②½(1+½)(1+¼)(1+1/16)(1+1/256)
③(2+1)(2²+1)(2&sup4;+1)(2&sup8;+1)(2¹6;+1)
①2(3+1)(3²+1)(3&sup4;+1)(3&sup8;+1)+1
②½(1+½)(1+¼)(1+1/16)(1+1/256)
③(2+1)(2²+1)(2&sup4;+1)(2&sup8;+1)(2¹6;+1)
①
2(3+1)(3^2+1)(3^4+1)(3^8+1)+1
= (3-1)(3+1)(3^2+1)(3^4+1)(3^8+1) + 1
= (3^2-1)(3^2+1)(3^4+1)(3^8+1) + 1
= (3^4-1)(3^4+1)(3^8+1) + 1
= (3^8-1)(3^8+1) + 1
= 3^16 - 1 + 1
= 3^16
②1/2 *(1+1/2)(1+1/4)(1+1/16)(1+1/256)
= (1-1/2)(1+1/2)(1+1/4)(1+1/16)(1+1/256)
= (1-1/4)(1+1/4)(1+1/16)(1+1/256)
= (1--1/16)(1+1/16)(1+1/256)
= (1-1/256)(1+1/256)
= 1-1/(256*256)
= 65535/65536
③(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)
= (2-1) (2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2-1)
= ……
= 2^32 -1
2(3+1)(3^2+1)(3^4+1)(3^8+1)+1
= (3-1)(3+1)(3^2+1)(3^4+1)(3^8+1) + 1
= (3^2-1)(3^2+1)(3^4+1)(3^8+1) + 1
= (3^4-1)(3^4+1)(3^8+1) + 1
= (3^8-1)(3^8+1) + 1
= 3^16 - 1 + 1
= 3^16
②1/2 *(1+1/2)(1+1/4)(1+1/16)(1+1/256)
= (1-1/2)(1+1/2)(1+1/4)(1+1/16)(1+1/256)
= (1-1/4)(1+1/4)(1+1/16)(1+1/256)
= (1--1/16)(1+1/16)(1+1/256)
= (1-1/256)(1+1/256)
= 1-1/(256*256)
= 65535/65536
③(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)
= (2-1) (2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)/(2-1)
= ……
= 2^32 -1
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