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Prove that $(1+\frac{1}{n})^k < 1+ \frac{k}{n}+\frac{k^2}{n^2}$

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#sequences-and-series #inequality #upper-lower-bounds
84
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Upper bound for $|\mathbb E[f(X)] - f(0)|$ when $X \sim N(0,\sigma^2)$ and $f:\mathbb R \to \mathbb R$ is piecewise-linear with $\|f'\|_\infty \le 1$.

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#real-analysis #probability-theory #upper-lower-bounds #gaussian-integral #concentration-of-measure
73
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What are some elementary bounds for Mertens' Third Theorem?

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#number-theory #prime-numbers #asymptotics #upper-lower-bounds
133
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Does the mean of $\log{\text{gpf}(n)}/\log{n}$ for the first $n$ naturals have a lower bound?

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#elementary-number-theory #prime-numbers #prime-factorization #upper-lower-bounds
439
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Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number?

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#upper-lower-bounds #conjectures #divisor-sum #arithmetic-functions #perfect-numbers
23
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Most Boolean Functions are Complex- Analysis Detail

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#computer-science #computational-complexity #upper-lower-bounds
33
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Parametrizing probability in Bernstein Inequality

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#probability-theory #inequality #upper-lower-bounds
2.8k
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Bound on l1 norm given bound on l2 norm

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#analysis #normed-spaces #upper-lower-bounds
34
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Upper bound of set

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#real-analysis #supremum-and-infimum #upper-lower-bounds
73
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Bound for a local maximum of a polynomial with integer coefficients?

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#real-analysis #analysis #inequality #polynomials #upper-lower-bounds
292
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MGF bound for non-centered random variables?

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#probability-theory #upper-lower-bounds #moment-generating-functions #concentration-of-measure
252
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Applying the Berry-Esseen theorem to non-identically distributed summands

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#probability-theory #asymptotics #upper-lower-bounds #central-limit-theorem #large-deviation-theory
159
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lower bound of $n(n-1)(n-2) \dots (n-k)$

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#inequality #permutations #combinations #upper-lower-bounds
92
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Is $\lim_{n \to \infty} n((1-\frac{1}{n})^n - \frac{1}{e}) = 0$?

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#sequences-and-series #convergence-divergence #upper-lower-bounds
51
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Inconclusive inequality result: show $(id - f)^{-1}$ is bounded

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#inequality #normed-spaces #upper-lower-bounds

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