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Candle height at half burn time
High school · ●●○○○ 20 pts
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. (The candle burns down each individual centimeter at a fixed rate.) Suppose it takes seconds for the candle to burn down completely. Compute the candle's height in centimeters seconds after it is lit.