Prove the following by the principle of mathematical induction:`1/2+1/4+1/8++1/(2^n)=1-1/(2^n)`

Explanation

To prove the statement \( S(n) : \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots + \frac{1}{2^n} = 1 - \frac{1}{2^n} \) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We need to check if the statement is true for \( n = 1 \).

**Left Hand Side (LHS)**:
\[
S(1) = \frac{1}{2}
...