Recent content by etaoin shrdlu

I haven't checked this, so I have probably gotten some of the regions of validity wrong, but here are my thoughts on approximating the sum. Write $N = \frac{\log a}{\log x}$ so that your series becomes $\sum_{n=0}^\infty \frac{x^n}{a+x^n} = \sum_{n=0}^\infty \frac{1}{1+x^{N-n}}$. Over all...

What about 00000 00111 11100 ? I second this suggestion. The search space is tiny, and if you're still looking for a proof, what you find may surprise you. What reasons do you have to believe that the statement is true?