Proof by induction concerning approximation algorithm for subset sum [closed]

Question

Assignment question

For algorithm APPROX-SUBSET-SUM, prove by induction on $i$ that for every element $y \in P_i$ that is at most the target sum $T$, there is a $z \in L_i$ such that

$$\frac{y}{(1+\frac{\epsilon}{2n})^i} \leq z \leq y$$

Here $\epsilon$ is the relative error bound, $P_i$ is the set of all subset sums of the first $i$ elements in the universe, and $L_i$ is the corresponding discretized set produced by APPROX-SUBSET-SUM.

My thoughts

I understand that proof by induction means that proving something for all natural numbers by first proving that it is true for $0$, and that if it is true for $n$ (or sometimes, for all numbers up to $n$), then it is true also for $n+1$. However, do I simply substitute $0$ and $n+1$ into $n$ and that would solve the question completely?