# A discrete time signal $x[n]$ is defined in terms of unit impulse function.Express the signal $x[n]$ in terms of step signal

A discrete time signal $$x[n]$$ is defined in terms of unit impulse function as follow

$$x[n]= 1-\sum_{r=3}^\infty \delta[n-1-r]$$

If $$x[n]$$ is expressed in terms of unit step function as $$x[n]=u[an-b]$$ then find the values of $$a$$ and $$b$$. I have tried to solve but not able to solve it further.please check image Please correct my grammer if there is any mistake.

Your result is correct, but it can be rewritten in an even simpler form, as suggested in the problem statement: $$x[n]=u[an+b]$$
If you draw the signal then you'll see that it is just a reversed and shifted unit step. From that drawing it should be easy to derive the constants $$a$$ and $$b$$.