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May
18
comment Does the infinite sum of $\sin(\frac{1}{n}+n\pi)$ converge or diverge?
Hint: how does $\sin(1/n+n\pi)$ relate to $\sin (1/n)$?
May
14
comment Prove that using generating function:For any $n ,k\in N$, the number of partitions of $n$ into parts
If you're being asked this, I suspect you've seen the generating-function proof for the case $k = 1$ - that is, that the number of partitions into parts which appear at most 1 time ("partitions into distinct parts") is the same as the number of partitions into parts not divisible by 2 ("partitions into odd parts"). Can you generalize this proof?
May
11
comment Find a linear reccurrence relation where a(n) is the number of subsets of {1,2,3,…,n} not containing three consecutive numbers.
This is a duplicate of math.stackexchange.com/questions/86249/… , although that question wasn't answered so I recommend leaving this one open.
Apr
29
comment If $n$ is composite, then $((n-1)!)^2 \equiv 0 \pmod n$
4 is the only counterexample: see e. g. Benoit Cloitre's comment at oeis.org/A046022
Apr
28
comment Find the probability of the following event
This, with slightly different numbers, is Kahneman and Tversky's taxicab problem: en.wikipedia.org/wiki/…
Apr
10
comment Compute $\sqrt[7]{0.999}$ to three decimal places.(From Gelfand's Algebra text.)
I don't agree with your assumption; my assumption is that Gelfand was looking for a smarter answer like mine, given that the numbers involved are so close to 1. (If he'd asked, say, to compute the cube root of 3.257, then I'd expect that he was looking for the long-multiplication answer.) But I can't prove this.
Feb
24
comment Is $\int_0^\infty x^{a-1} (1-x)^{b-1} e^{t-cx} dx$ integrable?
Thanks! I hadn't realized that your context was a beta distribution, and this was the first thing that came to mind.
Jan
30
comment Explain why catastrophic cancellation happens
I'm seeing the same thing in R. This supports the idea that this is an issue with floating-point numbers.
Jan
29
comment Why is Multiplicative Notation Used for Groups (Instead of Additive)?
I'm not sure I'd call this "multiplicative" notation - we don't explicitly write out the multiplication sign. I think that this is a case of juxtaposition having two meanings, multiplication (when used for numeric variables) and an arbitrary group operation.
Jan
20
comment Mathmatical notation for a term of a polynomial
I think that's the closest there is to a standard notation. (But I honestly wouldn't use it without definition unless speaking to an audience of people who deal with generating functions all the time.)
Jan
15
comment Find a quartic (degree 4) polynomial with integer coefficients whose roots are the primitive 12th roots of unity
The polynomial $(z-\alpha_1) (z-\alpha_2) \cdots (z-\alpha_n)$ has roots $\alpha_1, \alpha_2, \cdots, \alpha_n$.
Jan
14
comment Expectation of maximum of Binomial RVs
possible duplicate of Bounds for the maximum of binomial random variables
Jan
9
comment Visually stunning math concepts which are easy to explain
The basic idea is pretty simple: ${i \choose k} = {i \choose k-1} + {i-1 \choose k-1}$, and this recurrence holds $\mod p$ as well.
Jan
9
comment Visually stunning math concepts which are easy to explain
I'd also note that it's possible to compute ${i \choose k} \mod p$ without computing $i \choose k$. For large $i$ this would matter.
Dec
15
comment Taylor approximation for $\ln(1.3)$
Your book probably should say $0.255$.
Dec
15
comment Expected value of this deceptively simple variable
To find $E(Z)$: note that $Z$ is either 1, 0, or -1. With what probability does it take each of those values?
Dec
10
comment What is the probability that a Poisson random variable is prime?
Asymptotically I'd expect $Q(\lambda, 0)$ to be "the probability that a number near $\lambda$ is prime", i. e. about $1/\log \lambda$.
Dec
9
comment Can you select random entry from unknown number of entries?
If I recall correctly this is called "reservoir sampling", also worth googling.
Dec
8
comment Why is $\frac {1\cdot2\cdot3\cdot…\cdot n}{(n+1)(n+2)…(2n)}\le \frac 1 {n+1}$
See my edits to answer that question.
Dec
5
comment Chance on pairs when picking 'Sinterklaas tickets'
In the limit of large $n$, the number of 2-cycles of a permutation on $n$ elements is Poisson-distributed with mean $1/2$. (For $k$-cycles, it's $1/k$.) In particular, it's zero with probability $e^{-1/2}$. Restricting to derangements doesn't change this too much. This is a high-level explanation for the asymptotic result quoted in OEIS.