tag:blogger.com,1999:blog-2400513859305780710.post1848144454863839220..comments2023-04-04T07:53:53.789-07:00Comments on Mathematical Food For Thought: Condensation Sensation. Topic: Calculus/S&S.Jeffrey Wanghttp://www.blogger.com/profile/11114458640271201663noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2400513859305780710.post-64013441609693067342007-03-28T13:12:09.000-07:002007-03-28T13:12:09.000-07:00u spelled "iff" wrongu spelled "iff" wrongXuanhttp://www.xanga.com/xuannynoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-26032692244865207082007-03-28T13:28:10.000-07:002007-03-28T13:28:10.000-07:00iff = if and only if :Piff = if and only if :Ppaladin8noreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-38683053096429459382007-03-29T11:11:23.000-07:002007-03-29T11:11:23.000-07:00Hmm. I was going to ask for a proof, but it occur...Hmm. I was going to ask for a proof, but it occurred to me that (condensed series)t0rajir0unoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-85765101573290709412007-03-29T11:12:46.000-07:002007-03-29T11:12:46.000-07:00Oops. I wanted to write (condensed series) ≤ (ori...Oops. I wanted to write (condensed series) ≤ (original series) ≤ p * (condensed series). Yeah.<br><br>Anyway, Cauchy condensation gives<br><br>$ \displaystyle \sum_{n=2}^{\infty} \frac{p^n}{(n \ln p)^{n \ln p} } $<br><br>Which clearly converges by ratio test.t0rajir0unoreply@blogger.comtag:blogger.com,1999:blog-2400513859305780710.post-22277755866317111702007-03-29T14:33:04.000-07:002007-03-29T14:33:04.000-07:00The root test is also a good way to go to show con...The root test is also a good way to go to show convergence of that last thing.paladin8noreply@blogger.com