Mathematics
ZENG's user avatar
ZENG's user avatar
ZENG's user avatar
ZENG
  • Member for 5 years, 2 months
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All Questions Answers
Score Newest
answer
6
$2n! \geq (n-k)! n^{k-1} (2n+k-k^2)$
Nov 22, 2018
answer
6
Prove that if $a_k \in [0, 1] $ then $\frac {1}{1+a_1} + \frac {1}{1+a_2} + \cdots +\frac {1}{1+a_n} \le \frac{n}{1+ \sqrt[n]{a_1a_2\cdots a_n}}$.
Nov 29, 2018
question
5
Hard combinatorial identity: $\sum_{l=0}^p(-1)^l\binom{2l}{l}\binom{k}{p-l}\binom{2k+2l-2p}{k+l-p}^{-1}=4^p\binom{k-1}{p}\binom{2k}{k}^{-1}$
Jan 13, 2018
question
4
$(ab)^n = a^{n}b^{n}$ in a unitary ring $A$ implies A commutative?
Nov 27, 2018
question
3
6 points in the plane: Suppose that any triangle formed by three points will be similar to the triangle formed by the remaining three points.
Oct 9, 2018
question
3
$f: \mathbb{N}\cup\{0\} \longrightarrow \mathbb{N}\cup\{0\}, \forall x\in\mathbb{N}\cup\{0\}, f(x+1)+1 = f(f(x) + 1)$
Nov 3, 2020
question
2
Is the converse of Tychonoff's theorem true?
Mar 19, 2018
question
2
Stable under finite intersection
Oct 29, 2022
question
2
$p$ is adherent value of $\left(\sum_{i=1}^{p} z_{i}^n\right)_{n\in\mathbb{N}}$ where $z_{i}$ are complex of modulus 1
Nov 20, 2018
question
2
Function which can be extended to a $\mathcal{C}^k$ function for every $k\in\mathbb{N}$
Jan 17, 2022

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