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This Questions seems daunting but let’s put our thinking in order.

Let’s suppose that for some (n) there exist the desired numbers. we also assume that S1 <S2 <S3<…<Sn

surely S1 > 1 else (1- 1/S1) = 0

so we have 2 ≤ S1 ≤ S2–1 ≤ S3–2≤…Sn -(n-1) , hence Si ≥i+1 for each i = 1,2…n. Therefore

51/2010 = 17/670 =

So how do we approach this Q? one way is to have it as a function of (x) only and express it as

**g(x) = x^x + (1-x)^(1-x)** and then try to find the f’(x) =0 and solve the usual way… and you can see you’re headed to trouble. …

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A: As there is symmetry is the coefficients, first consider the…

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