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Note that 2^0 = 1 + 2^1 = 3 = 2^2 - 1 In general the sum of powers of 2 equal one less than 2 to the next power. Since 2048 is 2^11, 2047 is the sum of powers of 2 up to 2^10. (We start at 0, because n-i = 0 when i goes to n). So n= 10.
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