10-seconds challenge-7
For , the maximum value of the expression above is for some integer . Find .
This is a part of 10-seconds challenge .
The answer is 201.
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1 solution
Expression can be written as : x 1 0 0 1 + x 9 9 1 + ⋯ x 9 9 + x 1 0 0 1 Applying A M ≥ G M to denominator , we can see minimum value of denominator is 2 0 1 . Hence maximum value of expression is 2 0 1 1 , ∴ N = 2 0 1 . Equality occurs when x = 1 .