(AIME 1994) Find the positive integer n for which
[log2 1] + [log2 2] + [log2 3] +…+ [log2 n] = 1994
where [x] denotes the greatest integer less than or equal to x (for example [Π] = 3)
Solution:
Observe that:
[log2 1] = 0(20)
[log2 2] + [log2 3] = 1(21)
[log2 4] + [log2 5] + [log2 6] [...]
RP
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty” Bertrand Russell
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