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Nov
12
comment Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$
I like this better, but unfortunately, I am out of votes for today.
Nov
12
revised Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$
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Nov
12
answered Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$
Nov
12
revised Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$
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Nov
12
revised Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$
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Nov
12
answered Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$
Nov
12
revised Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$
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Nov
12
revised Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$
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Nov
12
comment Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$
btw, Mirzodaler: I am guessing you are just posting some interesting challenge problems you have come across. Please try to provide the source of the problems, whenever you can.
Nov
12
revised Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$
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Nov
12
comment Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$
@Chandru: I didn't see that comment until you pointed out!
Nov
12
answered Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$
Nov
12
comment Interesting calculus problems of medium difficulty?
Maybe not, was just guessing.
Nov
12
comment Interesting calculus problems of medium difficulty?
Continued fraction?
Nov
12
revised Convergence of $a_{0} = 0, a_{n}=f(a_{n-1})$ when $|f'(x)|\leq \frac{5}{6}$
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Nov
12
comment Measure of value of resources in a competitive game
Why has this got a close vote?
Nov
12
comment Checking if a number is a Fibonacci or not?
@QIao: Sorry I meant to say if you want to avoid floating point computations. With proper hardware support floating point computation are O(1). I am not claiming binary search is faster. It was mainly in response to "trusting" the results. strlen x is O(logx) btw.
Nov
12
revised Prove the sum of all numbers that do not have a multiplicative inverse mod $n$
attempting again.
Nov
12
comment Checking if a number is a Fibonacci or not?
@Qiao: Guess an $n$, compute $F_n$ (using matrix powers) and compare with $N$. If the entries are smaller, we need a bigger $n$, else smaller. This might be a bit slower, but that is the price you pay for avoiding floating point computations.
Nov
12
comment Convergence of $a_{0} = 0, a_{n}=f(a_{n-1})$ when $|f'(x)|\leq \frac{5}{6}$
Are you missing some condition on $f'(x)$? For instance take $f(x) = -100x + 1$. Perhaps $f'(x) \ge 0$?