Setting large candles on fire
Source: AIME II 2013, Problem 3
April 4, 2013
GaussAMCalgebraAIME
Problem Statement
A large candle is centimeters tall. It is designed to burn down more quickly when it is first lit and more slowly as it approaches its bottom. Specifically, the candle takes seconds to burn down the first centimeter from the top, seconds to burn down the second centimeter, and seconds to burn down the -th centimeter. Suppose it takes seconds for the candle to burn down completely. Then seconds after it is lit, the candle's height in centimeters will be . Find .