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

Show that this structure is an affinely regular polygon

Minimum percentage of a random variable within two bounds

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All Questions Answers
Score Newest
answer
29
Do there exist pairs of distinct real numbers whose arithmetic, geometric and harmonic means are all integers?
Apr 16, 2018
answer
20
Calculate a quartic monic polynomial given that $P(1)=10,P(2)=20$ and $P(3)=30$.
Apr 2, 2018
answer
18
Proving $(λ^d + (1-λ^d)e^{(d-1)s})^{\frac{1}{1-d}}\leq\sum\limits_{n=0}^\infty\frac1{n!}λ^{\frac{(d^n-1)d}{d-1}+n}s^ne^{-λs}$
Jan 27, 2018
answer
16
Maximum of $\int_a^b \frac{f(x)}{x}\,\mathrm dx$
Apr 24, 2019
answer
14
Prove $\lim\limits_{n\to∞}{\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-(x+1)})^{n+1}\over\sum\limits_{x=0}^n\binom nx(1+{\rm e}^{-x})^{n + 1}}=\frac 13$
Mar 9, 2018
answer
12
Prove $\sum\limits_{n=0}^\infty\frac{5^n(3^{5^{n+1}}-5\cdot3^{5^n}+4)}{(729)^{5^n}-(243)^{5^n}-5\cdot3^{5^n}+1}=\frac12$
Mar 3, 2018
question
11
How to compute the determinant of this Toeplitz matrix?
Dec 24, 2017
answer
11
Evaluating $\lim_{n \to \infty}\left(\sqrt{n^2 - n+1}-\left\lfloor\sqrt {n^2 - n+1}\right\rfloor\right)$
Oct 2, 2018
answer
10
If $a+b+c<0$ and $ax^2+bx+c=0$ has no real roots, is it true that $c$ must be less than $0$?
Mar 10, 2018
answer
9
If $f(f(x))+f(x)=x^4+3x^2+3$, prove that $f$ is even
Mar 20, 2018
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