Aryabhata
Reputation
56,813
397/400 score
 Nov12 revised Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ added 2 characters in body Nov12 answered Given $a_{1}=1, \ a_{n+1}=a_{n}+\frac{1}{a_{n}}$, find $\lim \limits_{n\to\infty}\frac{a_{n}}{n}$ Nov12 revised Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$ added 12 characters in body Nov12 revised Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$ added 2 characters in body Nov12 answered Exercise from Comtet's Advanced Combinatorics: prove $27\sum_{n=1}^{\infty }1/\binom{2n}{n}=9+2\pi \sqrt{3}$ Nov12 revised Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$ added 285 characters in body Nov12 revised Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$ added 53 characters in body; edited title Nov12 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. Nov12 revised Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$ added 560 characters in body; added 46 characters in body Nov12 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! Nov12 answered Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$ Nov12 comment Interesting calculus problems of medium difficulty? Maybe not, was just guessing. Nov12 comment Interesting calculus problems of medium difficulty? Continued fraction? Nov12 revised Convergence of $a_{0} = 0, a_{n}=f(a_{n-1})$ when $|f'(x)|\leq \frac{5}{6}$ edited title Nov12 comment Measure of value of resources in a competitive game Why has this got a close vote? Nov12 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. Nov12 revised Prove the sum of all numbers that do not have a multiplicative inverse mod $n$ attempting again. Nov12 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. Nov12 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 $f'(x) \ge 0$? Nov12 comment Convergence of $a_{0} = 0, a_{n}=f(a_{n-1})$ when $|f'(x)|\leq \frac{5}{6}$ +1 for showing the work done.