Functional Equations

I spotted this little book at the library and flipped through it. I saw the names Cauchy, Euler and d’Alembert and was immediately thinking “oh differential equations” until I flipped to this lovely nested square root
[tex]\sqrt{ 1+2 \sqrt{1+3\sqrt{1+4\sqrt{\ldots}}}}[/tex]
courtesy of Ramanujan.

This book turns out to be a guide to competition problem solving by Christopher Small. I’m not very big on competition problem solving, probably because I can’t do most of them, but I do like to work on some of them every once in a while. I’ve read most of the book, and quite like it.

Oh, the expression above evaluates to 3. Try it!

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