ques.....1+(1+a)x+(1+a+a2)x2+(1+a+a2+a3)x3+-----------
breaking up
(1+x+x2+x3......) + a (x+x2+x3+x4 .....) + a2 (x2+x3+x4+x5......) + ..........
=> (1+x+x2+x3......) + ax (1+x+x2+x3 .....) + a2x2 (1+x+x2+x3.....) + ..........
=> (1+x+x2+x3......).(1 + ax + a2x2 + a3x3 + ..........)
=> [1/(1-x)].[1/(1-ax)]
=>1/(1-x)(1-ax)