Question

计算 （a-b）^2n - 2(b-a)^2n-1 - 2/3 (b-a)^2n - 1/2(a-b)^2n-1

Answer 1

∵a=b-1

∴a-b=-1

（a-b）^2n - 2(b-a)^(2n-1)- 2/3 (b-a)^2n - 1/2(a-b)^(2n-1)

=(a-b)^2n+2(a-b)^(2n-1)-2/3(a-b)^2n-1/2(a-b)^(2n-1)

=1/3(a-b)^2n+3/2(a-b)^(2n+1)

=1/3(-1)^2n+3/2(-1)^(2n+1)

=1/3-3/2

=2/6-9/6

=-7/6