Since we need to take the sum of those things, and we can tell by looking at them that they're powers of two, we stick " sum of powers of 2" into the ALL KNOWING ORACLE. Now, if we factor out 20 units of food from those numbers (it's 5 * 4, which are just constants we've applied), we get a simple pattern: level 1 requires 1, level 2 requires 2, level 3 requires 4, level 4 requires 8, and so on if we can figure out a quick way to sum that up from level 1 to level 15, (or alternatively, from 2^0 to 2^14) then we just need to multiply everything by 20 and we'll have our answer. You need to feed a dragon four times before it levels, so we can factor that in and pretend it's already required - a level 1 dragon requires 5 * 4 = 20 units of food to level, a level 2 dragon requires 40, a level 3 dragon requires 80, and so on. Every level after that, the amount of food doubles - level 2 requires 10 food, level 3 requires 20 food, etc. Dragons start off at level 1, needing to be fed 5 units of food at a time.
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