reihe = (∑_(k = 1)^3) (Subscript[a, k]) (x^k)

inverse = (∑_(k = 0)^3) (Subscript[i, k]) (x^k)

Collect[
      Expand[inverse /. x -> reihe] /. {(x^n)_ /; n > 3 -> 0}, 
      x]