1. **State the problem:** Find the sum to infinity of the geometric progression (GP) 16 + 8 + 4 + 2 + ... 2. **Formula for sum to infinity of a GP:** The sum to infinity $S_\infty$ of a GP with first term $a$ and common ratio $r$ (where $|r| < 1$) is given by: $$S_\infty = \frac{a}{1-r}$$ 3. **Identify the first term and common ratio:** - First term $a = 16$ - Common ratio $r = \frac{8}{16} = \frac{1}{2}$ 4. **Check if sum to infinity exists:** Since $|r| = \frac{1}{2} < 1$, the sum to infinity exists. 5. **Calculate the sum:** $$S_\infty = \frac{16}{1 - \frac{1}{2}}$$ 6. **Simplify the denominator:** $$1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}$$ 7. **Substitute back:** $$S_\infty = \frac{16}{\frac{1}{2}}$$ 8. **Divide by a fraction (multiply by reciprocal):** $$S_\infty = 16 \times 2 = 32$$ **Final answer:** The sum to infinity of the GP is $32$.