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Ѕᴀᴀᴅ
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A bounty hunter

For all in the Math SE community: Enforcement of Quality Standards

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Proving $(λ^d + (1-λ^d)e^{(d-1)s})^{\frac{1}{1-d}}\leq\sum\limits_{n=0}^\infty\frac1{n!}λ^{\frac{(d^n-1)d}{d-1}+n}s^ne^{-λs}$

Prove $\lim\limits_{n\to∞}{\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-(x+1)})^{n+1}\over\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-x})^{n + 1}}=\frac 13$

Does $\sum\limits_{k=1}^n\frac{a_i-a_k}{a_i+a_k}\cdot\frac{a_j-a_k}{a_j+a_k}=0$ for all $i\neq j$ imply $a_1=a_2=\cdots=a_n$?

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Top posts
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12
How to make bold greek letters in Mathjax on Stackexchange?
Mar 16, 2019
answer
8
How to write h-bar (Planck constant divided by 2 $\pi$) using MathJax?
Apr 24, 2020
answer
8
How to do right alignment with MathJax?
May 30, 2021
answer
4
Left pointing vector accent
Sep 14, 2022
question
3
Mysterious space added in matrix-like environments
Mar 8, 2019
question
3
Why do some users citing compatibility issues when deprecating the use of Unicode characters?
Mar 24, 2019
question
3
Bug in "Saving" in the review process
Oct 26, 2022
question
2
Breaking daily limit of reviews [duplicate]
Mar 11, 2018
answer
2
Aligning own operator with limits in MathJax (bug or not?)
Jul 14, 2020
answer
1
How do I label the rows/columns of a matrix in MathJax?
Apr 27, 2020
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30
Do there exist pairs of distinct real numbers whose arithmetic, geometric and harmonic means are all integers?
20
Calculate a quartic monic polynomial given that $P(1)=10,P(2)=20$ and $P(3)=30$.
20
Proving $(λ^d + (1-λ^d)e^{(d-1)s})^{\frac{1}{1-d}}\leq\sum\limits_{n=0}^\infty\frac1{n!}λ^{\frac{(d^n-1)d}{d-1}+n}s^ne^{-λs}$
16
Maximum of $\int_a^b \frac{f(x)}{x}\,\mathrm dx$
14
Prove $\lim\limits_{n\to∞}{\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-(x+1)})^{n+1}\over\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-x})^{n + 1}}=\frac 13$