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As somebody used to say:

Does research. Smokes. Battles administration. Smokes. Wishes he could stop battling administration so that he could have more time to do research. Smokes some more.

The same. Except I do not smoke.


3,041 Answers

newest activity votes
304
Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$
87
$ \lim_{n \to \infty }\sin \sin …\sin n$
57
How do I define a bijection between $(0,1)$ and $(0,1]$?
34
What's the probability that a sequence of coin flips never has twice as many heads as tails?
33
Help with summing a power series
31
Expected time to roll all 1 through 6 on a die
29
How to compute the series $\sum\limits_{x=0}^\infty\sum\limits_{y=0}^\infty\sum\limits_{z=0}^\infty\frac{1}{2^x(2^{x+y}+2^{x+z}+2^{z+y})}$
25
Is there a formula for $(1+i)^n+(1-i)^n$?
25
How to derive a function to approximate $\sqrt{3}$?
24
Is the difference of the natural logarithms of two integers always irrational or 0?
24
Asymptotics of $1^n + 2^{n-1} + 3^{n-2} +\cdots + (n-1)^2 + n^1$
23
Given the pdf of independent RVs $I$ and $R$, how to find cdf of $W =I^2R$?
23
Are “sum” and “product” defined when there is only one number?
23
$\lim_{n\to\infty} \left(\frac{1^p+2^p+3^p + \cdots + n^p}{n^p} - \frac{n}{p+1}\right)$ Evaluating this limit
23
Tricky Integral
21
Compute $ \sum_{m=1}^{\infty} \sum_{n=1}^{\infty} \sum_{p=1}^{\infty}\frac{(-1)^{m+n+p}}{m+n+p}$
21
Explain $\iint \mathrm dx\mathrm dy = \iint r \mathrm d\alpha\mathrm dr$
21
Rule for multiplying rational numbers
20
How can I find $\lim_{n \to \infty}[(1-\frac{1}{2^2})(1-\frac{1}{3^2})\cdots(1-\frac{1}{n^2})]$
19
Finding $\sum_{n=1}^{9999} \frac{1}{(\sqrt{n+1}+\sqrt{n})(\sqrt[4]{n}+\sqrt[4]{n+1})} $
19
Proving an “amazing” claim regarding $\zeta( 3)$ and Apéry's proof
19
Evaluating $\lim_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$
18
Compute: $\lim_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{\frac{1}{2}}\cdots\left(1+\frac{n}{n}\right)^{\frac{1}{n}}$
17
Example that $\int |f(x)| dx=\infty$ but $\int |f(x)|^2 dx <\infty$
16
Finding $a_{2012}$
16
Apery's proof of the irrationality of $\zeta(3)$
16
Asymptotic behavior of $\sum\limits_{k=1}^{n}k^{1/4} $
16
Efficient computation of $E\left[\frac{1}{1+\sum_iX_i}\right]$ where $X_i$ is RV with Bernoulli distribution with different probabilities
15
Does the $\sum_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}$ converge?
15
Prove: $f(x)$ continuous function and $\int_a^\infty |f(x)|\;dx < \infty$ so $\lim_{ x \to \infty } f(x)=0$
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