Prove the identity: 1/i + S'/((1+S')ⁿ − 1) = (1 − PV)/i, given S'=i and PV=(1+i)^-n.

This problem asks us to prove an identity in financial mathematics. We need to show that the Left Hand Side (LHS) equals the Right Hand Side (RHS).

The identity to prove is:

$$\frac{1}{i} + \frac{S'}{(1+S')^n - 1} = \frac{1 - PV}{i}$$

From previous context, we assume $S' = i$.
Also, in financial mathematics, $PV$ typically refers to the present value of a single payment of 1 unit of money received in $n$ periods, which is $PV = (1+i)^{-n}$. Let's use this definition.

Step 1: Substitute $S' = i