The function fk : N $$ R$,$ where k $6=0$ is a parameter, is recursively

defined by

fk$(0)=0$

fk$($n$)=$ kfk$($n $1)+$ k $1$ for n $>0.$

Prove that, for all n $0,$ fk$($n$)=$ kn $1.$ Structure your proof as a proof by

structural induction, indicating where you make use of the inductive hypoth$-$

esis