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+

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.