Talk:Cauchy Condensation Test

If all the terms $a_n$ are positive, then why is the sequence of partial sums decreasing... It appears that the pictures need to be redrawn (with the dotted line more like the square root function). --Lord_Farin 12:33, 20 February 2012 (EST)
 * Sorry, the dotted line is a graph of $a_n$, not $\sum a_n$. I tried to fix every instance of my mistake, please double check. --GFauxPas 12:39, 20 February 2012 (EST)
 * I think the best way to look at the geometric proof is to view the series as a sum of each term in the sequence times one, so you get lots of rectangles of width one that are smaller than the rectangles of the condensed sequence.. If I actually drew that it would be too hard to read the diagram, but now that I think about it it's not that obvious from the current presentation. Suggestions? --GFauxPas 12:59, 20 February 2012 (EST)
 * I get it; I think that's cleared now. Minor suggestion would be to use the letter $a$ instead of $f$, as to avoid possible confusion on what it means. --Lord_Farin 13:03, 20 February 2012 (EST)
 * I considered that, but I wasn't sure if $a_{2^n}$ was readable enough. Or perhaps you mean $a\left({2^n}\right)$? --GFauxPas 13:04, 20 February 2012 (EST)
 * The latter. I understood you did it for readability indeed. --Lord_Farin 13:08, 20 February 2012 (EST)
 * I edited the proof to explicitly tell the reader about the implied rectangles with width 1. If you can think of a way to make it clearer, please do so. --GFauxPas 13:16, 20 February 2012 (EST)