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From: D Tao on 4 Jun 2010 10:35
Hi all,

Let n>=2 be an integer, and let R,V be integers satisfying 0<=V<=n,
1<=R<=n and R+V<=n.

It appears to be that the function f(R,V) = V ((R+1)^n - R^n) / n^n <=
3/4 for all R,V above. How might I prove this? Substituting the bound
V<=n-R and then differentiating to find a stationary point leaves me a
polynomial in degree n-1 to find a root of. Clearly not viable.

Any help appreciated.

Regards,
David
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