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This one, by Oleg Golberg, appeared in the $6^{th}$ issue of Mathematical Reflections (MR) 2007. I don’t have a solution yet, but I think I should be able to solve it sooner or later. If you find a solution, you should send it to MR by Jan 19. Here is the problem anyway.

For all integers $k, n \geq 2$, prove that $\\ \displaystyle \sqrt[n]{1 + \frac{n}{k}} \leq \frac1{n} \log \big( 1+\frac{n}{k-1} \big) + 1.$

I became interested in mathematical blogging after visiting Terence Tao’s and Timothy Gower’s blogs on numerous occasions. It seems there is a sizable number of mathematicians disseminating valuable information through their blogs, and I see this as a healthy sign. Such blogs provide a wealth of information to students like me, and dare I say, I learn most of my math from such blogs!

I intend to write about math mostly as an exercise in exposition. I am assuming this will be of great help to me later on. I also will be posting some problems in the “Problem Corner” section every now and then.

Let’s see how this goes. I am hoping my enthusiasm for blogging will not wear off too soon!

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