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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?
Nov
13
answered How to calculate the expected number of distinct items when drawing pairs?
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: Do you have any guess as to what the limit could be?
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: As promised :-)
Nov
13
answered What could the notation $l^\infty(\mathcal{F})$ mean, where $\mathcal{F}$ is a set of measurable functions?