If ∑r=0n ar(x−α+2)r−br(α−x−1)r=0, then

Let α−x−1=t.Then ∑r=0n ar(1−t)r=∑r=0n brtr⇒ bn= coefficient of tn in ∑r=0n ar(1−t)r           = coefficient of tn in an(1−t)n=(−1)n×an