写出简便计算过程第一题(1/2+1)*(1/4+1)*(1/16+1)*(1/256+1)第二题(a+b+c)3-(b+c-a)3-(c+a-b)3-(a+b-c)3证明题:已知x+y=u+v,x2+y2=u2+v2求证:x2008+y2008=u2008+v2008
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![写出简便计算过程第一题(1/2+1)*(1/4+1)*(1/16+1)*(1/256+1)第二题(a+b+c)3-(b+c-a)3-(c+a-b)3-(a+b-c)3证明题:已知x+y=u+v,x2+y2=u2+v2求证:x2008+y2008=u2008+v2008](/uploads/image/z/8670988-28-8.jpg?t=%E5%86%99%E5%87%BA%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%E8%BF%87%E7%A8%8B%E7%AC%AC%E4%B8%80%E9%A2%98%281%2F2%2B1%29%2A%281%2F4%2B1%29%2A%281%2F16%2B1%29%2A%281%2F256%2B1%29%E7%AC%AC%E4%BA%8C%E9%A2%98%28a%2Bb%2Bc%293-%28b%2Bc-a%293-%28c%2Ba-b%293-%28a%2Bb-c%293%E8%AF%81%E6%98%8E%E9%A2%98%EF%BC%9A%E5%B7%B2%E7%9F%A5x%2By%3Du%2Bv%2Cx2%2By2%3Du2%2Bv2%E6%B1%82%E8%AF%81%EF%BC%9Ax2008%2By2008%3Du2008%2Bv2008)
写出简便计算过程第一题(1/2+1)*(1/4+1)*(1/16+1)*(1/256+1)第二题(a+b+c)3-(b+c-a)3-(c+a-b)3-(a+b-c)3证明题:已知x+y=u+v,x2+y2=u2+v2求证:x2008+y2008=u2008+v2008
写出简便计算过程
第一题(1/2+1)*(1/4+1)*(1/16+1)*(1/256+1)
第二题(a+b+c)3-(b+c-a)3-(c+a-b)3-(a+b-c)3
证明题:已知x+y=u+v,x2+y2=u2+v2求证:x2008+y2008=u2008+v2008
写出简便计算过程第一题(1/2+1)*(1/4+1)*(1/16+1)*(1/256+1)第二题(a+b+c)3-(b+c-a)3-(c+a-b)3-(a+b-c)3证明题:已知x+y=u+v,x2+y2=u2+v2求证:x2008+y2008=u2008+v2008
第一题(1/2+1)*(1/4+1)*(1/16+1)*(1/256+1)
=(1-1/2)(1+1/2)(1+1/4)...(1+1/256)/(1-1/2)
=(1-1/4)(1+1/4)...(1+1/256)/(1/2)
=...
=(1-1/256)(1+1/256)*2
=2(1-1/65536)
第二题(a+b+c)3-(b+c-a)3-(c+a-b)3-(a+b-c)3
(a+b+c)^3-(b+c-a)^3-(c+a-b)^3-(a+b-c)^3
=[(a+b+c)^3-(b+c-a)^3]-[(c+a-b)^3+(a+b-c)^3]
=[(a+b+c)-(b+c-a)][(a+b+c)^2+(a+b+c)(b+c-a)+(b+c-a)^2]-[(c+a-b)+(a+b-c)][(c+a-b)^2-(c+a-b)(a+b-c)+(a+b-c)^2]
=2a[2a^2+2b^2+2c^2+4bc+(b+c)^2-a^2]-2a[2a^2+2b^2+2c^2-4bc+(b-c)^2-a^2]
=2a(3b^2+3c^2+a^2+4bc)-2a(3b^2+3c^2+a^2-4bc)
=8bc+8bc
=16bc.