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1d
comment Limit of the sequence $\lim_\limits{n\to\infty}\sin(2\pi(n^2+n^{1/2})^{1/2})$.
Yes, that does it. Alternatively (Taylor seems like overkill for this to me), note that $\sqrt{1+x} < 1+x/2$, so $\sqrt{1+n^{-3/2}} - 1 < {1 \over 2} n^{-3/2}$.
1d
answered Limit of the sequence $\lim_\limits{n\to\infty}\sin(2\pi(n^2+n^{1/2})^{1/2})$.
1d
comment Limit of the sequence $\lim_\limits{n\to\infty}\sin(2\pi(n^2+n^{1/2})^{1/2})$.
In this case, yes. There is no limit if $n$ is a real number but there is if $n$ is an integer.
1d
comment Limit of the sequence $\lim_\limits{n\to\infty}\sin(2\pi(n^2+n^{1/2})^{1/2})$.
Do you mean for $n$ to be an integer or a real number?
1d
comment Question on meaning of a symbol: long thin C
They don't. In fact the second edition of Stanley (www-math.mit.edu/~rstan/ec/ec1) uses the $[z^n] f(z)$ notation (see p. 11).
Feb
5
answered Proof of divisibility: $17 \mid 3 \cdot 5^{2015} + 2^{2017} \cdot 5^{670}$
Feb
3
answered How to calculate number combinations of formulas for a number of propositions
Feb
2
comment Limit in number theory
This would get down to $c = 1/2 + \epsilon$ as well.
Jan
29
comment Expected value of sum of cards
This seems a bit tricky to get an exact answer to but simulation would be easy. Do you need an exact answer or just an approximate one?
Jan
28
comment Pair of consecutive squarefree numbers with $n$ distinct prime factors
This is related to oeis.org/A052215 (which unfortunately doesn't give any results beyond what's figured out in the answers to this question).
Jan
27
comment How many numbers are there of 2n digits that the sum of the digits in the first half equals the sum of the digits in the second half
I believe you mean the Central Limit Theorem, not the Law of Large Numbers, but this is the first thing that came to mind for me as well.
Jan
27
answered Number of ways to roll five 6-sided dice with sum 7
Jan
27
comment 1995 USAMO Problems/Problem 2
You seem to be referring to a solution that's out there somewhere - can you link to it?
Jan
26
answered First Fibonacci Number with Given Remainder
Jan
25
answered Distance between the nullpoints of the series of derivatives of ln(x)/x
Jan
25
comment What inversion sets of permutations of $123\ldots n$ are possible?
A comment (although I'm not sure how to get from this to an answer): every permutation of $123 \cdots n$ has a different inversion set.
Jan
22
comment Prove that $\frac{2^{122}+1}{5}$ is a composite number
$1709 = 14*122 + 1$ is also a factor, as is $3456749$. (I am not inspired - I found these by trial division.)
Jan
21
revised Find the value of $\log_{xz}(xy^4z) \times \log_{xy}(xyz^4)$
removed recreational-mathematics tag
Jan
20
answered Is the sum of random variables X and X 2X?
Jan
19
answered What's the period of $\sin \left(x^\frac{3}{2}\right)$?