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.

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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.
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.

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.
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-1
a-b=-1
所以原式=(1/3)(-1)^2n+(3/2)(-1)^(2n-1)
=1/3-3/2
=-7/6