This question reminded me of a better one: Prove that

Spoiler:

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- May 15th 2009, 03:42 AMNonCommAlgAn upper bound for a series
This question reminded me of a better one: Prove that

__Spoiler__: - Jun 1st 2010, 10:51 PMchiph588@
I'll prove what's in the spoiler box (the stronger result):

We need to be careful about in the line above. This is just one value though, so check it manually and assume .

Now let's find the maximum of .

so solving we see .

But a little work shows which proves the claim.

**p.s.**I'm sure there's a much more elegant proof.