Aryabhata
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60,464
416/400 score
 Nov 14 comment Does the series $\sum\limits_{n=1}^{\infty}\frac{\sin(n-\sqrt{n^2+n})}{n}$ converge? +1 for showing the effort. Nov 14 comment How to calculate the expected number of distinct items when drawing pairs? +1: For the effort! Nov 14 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: No need to forget, it actually can be made to work! Nov 14 comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ you need a little more steps to get rid of Sum (1/a_k_^2) Nov 14 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 :-) Nov 14 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 :-) Nov 14 awarded calculus Nov 14 comment Finding a closed form for an infinite product Please choose a better title. Nov 13 revised Finding a closed form for an infinite product added 32 characters in body Nov 13 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 :-) Nov 13 revised Finding a closed form for an infinite product edited body Nov 13 answered Finding a closed form for an infinite product Nov 13 awarded Nice Answer Nov 13 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. Nov 13 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. Nov 13 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. Nov 13 revised How to calculate the expected number of distinct items when drawing pairs? added 71 characters in body; deleted 82 characters in body Nov 13 comment How to calculate the expected number of distinct items when drawing pairs? @Ross: You are right. I was assuming with replacement. Nov 13 revised How to calculate the expected number of distinct items when drawing pairs? added 56 characters in body Nov 13 comment Prove f is an integrable map Looks like homework. What you have tried?