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Feb
6
comment $α_n= \cos^{21}(n\pi/3)+\sin^{32}(n\pi/3)+11 $ has a convergent and oscillating sub sequence?
There are no more than $6$ different numbers in the sequence (actually there are fewer because the sine occurs to an even power). So there are fewer than $6$ limit points of subsequences. It is not true that every point in $[10,13]$ is a limit point.
Feb
6
comment Solve …
You are welcome. Well, the answer was wrong, it should be $13$.
Feb
6
comment Solve …
I agree. The answer is wrong, and certainly $|x_1+x_2|$ would make it right, but that is not what they asked for.
Feb
6
comment permutations of a 3 object
@IanColey: There is no repetition. For example, $(1,2,3)$ is intended to be the permutation that sends $1$ to $1$, $2$ to $2$, and $3$ to $3$. (Not a good choice of notation! Conflicts badly with the standard cycle notation.)
Feb
6
comment Solve …
There is a second possibility that you found but did not analyze, namely $x=4y$. That does satisfy the first equation. Proceed like you did with the extraneous $y=4x$.
Feb
6
revised Solve …
added 127 characters in body
Feb
6
answered Solve …
Feb
6
comment Combination - Probability. Probability within a set of 2
I thought hat having a comment and an answer was overkill. The answer became Community wiki for reasons mysterious to me. The other answer (particular couple) interprets the question in a different manner. As mentioned in comments, the question is somewhat imprecise.
Feb
6
comment Proof of irrationality of $\dfrac{\sqrt{8}}{\sqrt{7}}$
You are welcome. It might have been easier if you did not have the componendo et dividendo tool, which used to be a standard item in school algebra, but is now infrequently taught.
Feb
6
answered Proof of irrationality of $\dfrac{\sqrt{8}}{\sqrt{7}}$
Feb
6
answered Combination - Probability. Probability within a set of 2
Feb
6
comment A formula for a sequence which has three odds and then three evens, alternately
$1,1,1,0,0,0,1,1,1,\dots$.
Feb
6
comment $2+3+5+9+8+15+11+21+14+27+17+\dots$
The $2,5,8,\dots$ part has $n+1$ terms.
Feb
6
reviewed Approve Prove that a number is even, given the cube is even
Feb
6
answered probability of $3$ numbers out of $49$ in a lottery
Feb
6
comment probability of $3$ numbers out of $49$ in a lottery
Does the Lottery Corporation select $10$ numbers?
Feb
6
comment Integral relationship problem
Make the change of variable $u=x^2$.
Feb
6
answered Recursive formula for tiling checkerboard
Feb
6
comment Two species are competing in a region for control of a limited resource
On average the amount controlled by $X$ is indeed $0.5$. But imagine cutting a rod of length $1$ into $2$ parts, with uniform distribution. The length of the larger part will never, or hardly ever, be exactly $0.5$, and often it will be much bigger. So the average size of the larger part should be substantially bigger than $0.5$.
Feb
6
answered Finding the area of a portion of circle