Question

若(x-2)^9 = a0 + a1 (x-1) + a2 (x-1)^2 + ...+ a9 (x-1)^9 ,则 a

Answer 1

(x-2)^9=(x-1-1)^9 =a0 + a1 (x-1) + a2 (x-1)^2 + ...+ a9 (x-1)^9 ,所以a8(x-1)^8=C(9,8)(x-1)^8*(-1)^1 =-C(9,1)(x-1)^8 =-9(x-1)^8 即a8=-9