Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

algebra intermediate

Problem

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?
Solution
On the second, third, fourth, and fifth trips, you eat , , , and of the pizza, respectively. The total portion of the pizza eaten is the geometric series
Final answer
\frac{31}{32}