The given mathematical equation represents the sum of a geometric series.
A geometric series is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'common ratio'. In this case, the common ratio is 1/2.
The given equation is a sum (∑) from i = 1 to n of the terms 1/2^i, equal to 1 - (1/2^n).
The left hand side represents the sum of the series, it could be calculated easily step by step.
For example, if we choose n = 3, then the sum is: 1/2^1 + 1/2^2 + 1/2^3.
So ∑ _{i=1}^{3} of 1/2^i = 0.5 + 0.25 + 0.125 = 0.875.
On the right hand side of the equation, the term (1 - 1/2^n) is calculated also straightforwardly.
Still taking n = 3 as an example, it results in: 1 - 1/2^3 = 1 - 0.125 = 0.875.
This equation can be proved true for all n >= 1. Since both sides yield the same result, it confirms that the sum of the geometric series ∑ _{i=1}^{n} 1/2^i is indeed equal to 1 - 1/2^n for any n greater or equal to 1.