If the expansion in powers of x of the function 1(1−ax)(1−bx) is a0+a1x+a2x2+a3x3+…then αnis

∵ (1−ax)−1(1−bx)−1=1+ax+a2x2+…1+bx+b2x2+…∴ an= coefficient of xn in (1−ax)−1(1−bx)−1=a0bn+abn−1+…+anb0=a0bn1+ab+ab2+…=a0bnabn+1−1ab−1=bnan+1−bn+1a−b⋅bbn+1=an+1−bn+1a−b