Understand the first term, (1)/(i).

• This term represents the present value of a perpetuity. A perpetuity is a series of equal payments that continue indefinitely. If you receive 1 unit of money at the end of each period forever, and the interest rate per period is $i$, then the present value of all those future payments is $\frac{1}{i}$.

• This term is related to the future value of an ordinary annuity. The formula for the future value of an ordinary annuity of 1 unit of money per period for $n$ periods at an interest rate $i$ is $s_{\overline{n}|i} = \frac{(1+i)^n - 1}{i}$.
• Therefore, the term $\frac{1}{(1+i)^n - 1}$ can be written as $\frac{1}{i \cdot s_{\overline{n}|i}}$. It represents the reciprocal of the future value of an annuity of 1 per period, multiplied by $i$. This is not a standard standalone financial factor.

To add the two fractions, we find a common denominator, which is $i((1+i)^n - 1)$.

Multiply the numerator and denominator of the first term by $((1+i)^n - 1)$:

Multiply the numerator and denominator of the second term by $i$:

Now, add the two fractions:

This is the simplified form of the Left Hand Side.