Question

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

Answer 1

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