marty cohen
  • Member for 10 years, 6 months
  • Last seen this week
19 answers
110 votes
10k views
69 bookmarks
What is the most unusual proof you know that $\sqrt{2}$ is irrational?
7 answers
96 votes
33k views
48 bookmarks
Why is $\frac{987654321}{123456789} = 8.0000000729?!$
1 answers
65 votes
2k views
20 bookmarks
Are the sums $\sum_{n=1}^{\infty} \frac{1}{(n!)^k}$ transcendental?
3 answers
58 votes
3k views
12 bookmarks
What proportion of positive integers have two factors that differ by 1?
6 answers
51 votes
6k views
24 bookmarks
Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?
16 answers
42 votes
2k views
13 bookmarks
Literary statements that are false as mathematics
21 answers
38 votes
3k views
23 bookmarks
What is the most surprising result that you have personally discovered?
5 answers
36 votes
2k views
22 bookmarks
How close can $\sum_{k=1}^n \sqrt{k}$ be to an integer?
1 answers
29 votes
2k views
15 bookmarks
Is this proof of the infinitude of primes valid?
2 answers
25 votes
662 views
12 bookmarks
Are there an infinite number of primes of the form $\lfloor \pi n \rfloor$?
2 answers
14 votes
779 views
2 bookmarks
If $u_1=1$ and $u_{n+1} = n+\sum_{k=1}^n u_k^2$, then $u_n$ is never a square.
1 answers
13 votes
256 views
1 bookmarks
Possible generalizations of $\sum_{k=1}^n \cos k$ being bounded
4 answers
12 votes
477 views
4 bookmarks
For what $n$ can $\pm 1\pm 2\pm 3 ... \pm (n-1) \pm n = n+1$?
3 answers
12 votes
4k views
3 bookmarks
What is the most elementary proof that $\lim_{n \to \infty} (1+1/n)^n$ exists?
3 answers
12 votes
188 views
3 bookmarks
Prove that $\prod_{k=1}^{\infty} \big\{(1+\frac1{k})^{k+\frac1{2}}\big/e\big\} = \dfrac{e}{\sqrt{2\pi}}$
2 answers
11 votes
237 views
6 bookmarks
What is the asymptotic expansion of $x_n$ where $x_{n+1} = x_n+1/x_n$?
2 answers
11 votes
268 views
3 bookmarks
What can be said about $\prod_{s=2}^{\infty} \zeta(s) $?
2 answers
11 votes
359 views
7 bookmarks
Prove $\sum_{k=0}^n \binom{n}{k}(-1)^k \frac{x}{x+k} = \prod_{k=1}^n \frac{k}{x+k}$ and more
2 answers
10 votes
266 views
2 bookmarks
Which is the better approximation to $e$?
0 answers
8 votes
111 views
2 bookmarks
Show that $\ln(\ln(n))$ is not rational for all integers $n\geq2$
0 answers
8 votes
109 views
2 bookmarks
A conjecture about “equiharmonic numbers” of Flajolet via Doron Zeilberger
2 answers
8 votes
619 views
1 bookmarks
Find conditions on positive integers so that $\sqrt{a}+\sqrt{b}+\sqrt{c}$ is irrational
4 answers
7 votes
3k views
4 bookmarks
Prove that $n^k < 2^n$ for all large enough $n$
1 answers
7 votes
101 views
On the asymptotics of $\sum_{k=1}^{n^2} \{\sqrt{k}\} $
3 answers
6 votes
126 views
1 bookmarks
Show that $\sum_{k=1}^{\infty}\frac{2^{-k}}{k}=\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{k}$ without evaluating either sum
1 answers
6 votes
103 views
Which sets of base 10 digits have the property that, for every $n$, there is a $n$-digit number made up of these digits that is divisible by $5^n$?
2 answers
6 votes
64 views
2 bookmarks
Show that if $f$ increases nicely and $x > 1$ then $\lim_{n \to \infty}\frac{f(n)}{x^n}\sum_{k=1}^n \frac{x^k}{f(k)} = \frac{x}{1-x}$
0 answers
6 votes
83 views
5 bookmarks
Show there are only a finite number of integers with $\dfrac{\prod_{i=1}^n a_i-1}{\prod_{i=1}^n (a_i-1)} $ an integer
1 answers
6 votes
191 views
1 bookmarks
If $\frac{p_{n+1}}{np_n} \to p > 0 $, then $\sqrt[n+1]{p_{n+1}}-\sqrt[n]{p_{n}} \to \frac{p}{e}$
1 answers
6 votes
392 views
1 bookmarks
How many different ways can the signs be chosen so that $\pm 1\pm 2\pm 3 ... \pm (n-1) \pm n = n+1$?
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