Aryabhata
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 Nov14 comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ @daniel: How did you get rid if Sum (1/a_k_^2) ? btw 2 is correct :-) Nov14 comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ Very interesting. Well done :-) Nov14 awarded calculus Nov14 comment Finding a closed form for an infinite product Please choose a better title. Nov13 revised Finding a closed form for an infinite product added 32 characters in body Nov13 comment Finding a closed form for an infinite product @sivaram: Thanks! This is a well known trick, though, and according to the wiki apparently dates back to Euler. I am pretty sure this has been rediscovered a million times since then :-) Nov13 revised Finding a closed form for an infinite product edited body Nov13 answered Finding a closed form for an infinite product Nov13 awarded Nice Answer Nov13 comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ +1: Even though this seems like nonsensical math, Donald J Newman actually suggests using this as a quick method to get an idea of the rough asymptotic behaviour of a series. Nov13 comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ @daniel: I would strongly suggest you try guessing the limit first. Hint for that: read all the answers/comments in this thread again :-) btw, if your professor gives a solution which does not require guessing the solution at all, please let us know. I am curious. Nov13 comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ @daniel: 3 is not right. Why don't you try computing a few more values? Did the problem give any hints you could use? What tools do you have available? I am curious though, which course is this? Perhaps a link to the course webpage. Nov13 revised How to calculate the expected number of distinct items when drawing pairs? added 71 characters in body; deleted 82 characters in body Nov13 comment How to calculate the expected number of distinct items when drawing pairs? @Ross: You are right. I was assuming with replacement. Nov13 revised How to calculate the expected number of distinct items when drawing pairs? added 56 characters in body Nov13 comment Prove f is an integrable map Looks like homework. What you have tried? Nov13 answered How to calculate the expected number of distinct items when drawing pairs? Nov13 comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ @daniel: Do you have any guess as to what the limit could be? Nov13 comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ +1: As promised :-) Nov13 answered What could the notation $l^\infty(\mathcal{F})$ mean, where $\mathcal{F}$ is a set of measurable functions?