All parts would be greatly appreciated, i tried working it out but i do not know if the process i used was correct

3. Linear appruximatinn. Write dew-a the linear appreximatiena {a} [if r I} am at [l [h] Elf a I} am at l [e] [H m IJr {1 + a)\" at El, fer a. an arbitrary peaitive integer. {:1} er a H mm 1) at a