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19
How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$?
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17
coin toss question
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16
Integral of $\frac{1}{(1+x^2)^2}$
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16
What is the purpose of Stirling's approximation to a factorial?
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15
Prove that $\sum_{k=1}^{\infty} \large\frac{k}{\text{e}^{2\pi k}-1}=\frac{1}{24}-\frac{1}{8\pi}$
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14
What is the 'implicit function theorem'?
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13
$\sum \frac{1}{f(k)}$ converges iff $\sum \frac{f^{-1}(k)}{k^2}$ converges
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13
Power Series with the coefficients $n!/(n^n)$
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12
An Alternate Proof to a Theorem Involving “e”
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11
Energy norm. Why is it called that way?
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11
Sophistication of Series[…]
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11
An apparently “simple” limit?
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9
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
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9
Integrate in Mathematica takes forever
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9
How to calculate $\int_{-a}^{a} \sqrt{a^2-x^2}\ln(\sqrt{a^2-x^2})\mathrm{dx}$
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8
Simulating uniformly on $S^1=\{x \in \mathbb{R}^n \mid \|x\|_1=1\}$
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8
$T(1) = 1 , T(n) = 2T(n/2) + n^3$? Divide and conquer
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8
Proof that $t-1-\log t \geq 0$ for $t > 0$
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8
Differential equation $xy^3y'=2y^4+x^4$
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8
$\int_{0}^{\pi}\left|\frac{\sin nx}{x}\right|~dx \geq \frac{2}{\pi}(1+\frac{1}{2}+ \cdots +\frac{1}{n})$
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7
Inequality on balls/bins with nested logs
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7
Limit of $\lim_{x \to\infty} 3\left(\sqrt{\strut x}\sqrt{\strut x-3}-x+2\right)$
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7
How to prove absolute summability of sinc function?
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7
Finding all the critical points of $f(x,y) = (5x+7y-25)e^{-(x^2 + xy + y^2)}$
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7
An integral Lobachevsky calculated incorrectly
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7
Series of nested integrals
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7
Finding an Explicit Formula from the Recurrence: $na_{n}= 2 ( a_{n-1}+a_{n-2})$
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7
Is $\int_0^t \left[f(x)-g(x) + l\right]\mathrm dx > \int_t^1 \left[f(x-t)-f(x)\right] \mathrm dx$?
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7
Fun calculus problem I can't seem to solve
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7
If $A\in M_{n}(\mathbb{C})$ is a Hermitian matrix so $I-iA$ is Invertible
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