化简求值,（a-b)[2n次幂]-2(b-a)[2n-1次幂]-2/3(b-a)[2n次幂]-1/2(a-b)[2n-1次幂],其中a=b-1,n为正整数.

题目

化简求值,（a-b)[2n次幂]-2(b-a)[2n-1次幂]-2/3(b-a)[2n次幂]-1/2(a-b)[2n-1次幂],其中a=b-1,n为正整数.

答案

2n是偶数,2n-1是奇数所以(b-a)^(2n-1)=-(a-b)^(2n-1)(b-a)^2n=(a-b)^2n所以原式=(a-b)^2n+2(a-b)^(2n-1)-2/3(a-b)^2n-1/2(a-b)^(2n-1)=(1-2/3)(a-b)^2n+(2-1/2)(a-b)^(2n-1)=(1/3)(a-b)^2n+(3/2)(a-b)^(2n-1) a=b-1a...