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 Oct 7 awarded Popular Question Feb 4 awarded Critic Feb 4 comment Third axiom of topology I'm sorry. I didn't mean to accuse anyone of anything. I wasn't actually aware that MOOC homework questions were a violation to begin with. I was just explaining how I knew what Sananth meant. Feb 4 comment Third axiom of topology This is a homework problem in a Coursera course. Sanath means "3rd axiom of separation" not "3rd axiom of topology." The 3rd axiom (in this development) is separation of a point and a closed set by disjoint open sets. So, his alternate formulation is equivalent and the question is why? Dec 5 awarded Popular Question May 24 awarded Yearling Aug 16 answered Infinite series expansion of $\sin (x)$ Jun 22 awarded Enthusiast Jun 6 comment Inscribed kissing circles in an isosceles trapezoid The height of the inner trapezoid isn't the diameter of the circles, but it's still easy to figure out. Jun 6 awarded Teacher Jun 6 answered Inscribed kissing circles in an isosceles trapezoid May 31 comment Power series of $\ln(x+\sqrt{1+x^2})$ without Taylor thanks again. This clears things up to the point where I understand the solution, but I'm still uneasy with it. Squaring a power series isn't something that's been discussed in the book yet. It (multiplying power series, that is) is in an optional section about two sections further from where this problem was found. Can you conceive of any other way to solve this problem? May 31 awarded Supporter May 31 comment Power series of $\ln(x+\sqrt{1+x^2})$ without Taylor @TonkyK, Thank you very much for your answer. Thank you as well, @miracle173. I found the expansion you suggested that I use in my book. It's derived as a result of Taylor's formula in a section that I haven't gotten to yet. Is there some other way to derive the binomial series or is there some way to solve this problem without it? Thanks again. May 31 asked Power series of $\ln(x+\sqrt{1+x^2})$ without Taylor May 25 awarded Nice Question May 24 answered What is the area of the portion of 1/8 of an sphere cut off by two parallel planes? May 24 awarded Editor May 24 revised The sum of $(-1)^n \frac{\ln n}{n}$ I added the answer May 24 awarded Student