You have a whole pizza in the refrigerator. On your first trip to the refrigerator, you eat half the pizza. On each successive trip, you eat half of the remaining pizza. After five trips to the refrigerator, what fractional part of the pizza have you eaten?

ant101 Dec 27, 2018

#1**+2 **

This is just a geometric series, so the answer is:

\(\begin{align*} \frac12+\frac1{2^2}+\frac1{2^3}+\frac1{2^4}+\frac1{2^5} &= \frac{\frac12\left(1-\left(\frac12\right)^5\right)}{1-\frac12}\\ &=1-\left(\frac12\right)^5\\ &=1-\frac1{32}\\ &=\boxed{\frac{31}{32}}. \end{align*}\)

tertre Dec 27, 2018