Mathematics
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  • Member for 1 year
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All Questions Answers
Score Newest
question
3
De Moivre's Theorem: prove that $\sum_{j=0}^{50}(-1)^j\binom{101}{2j}\cos^{101-2j}(\frac {\pi}{101})\sin^{2j}(\frac {\pi}{101})=-1$
Mar 19, 2022
question
1
Prove $\left(\frac{u+v}{2}\right)^p\leq\frac{u^p+v^p}{2}$ [duplicate]
Mar 20, 2022
question
1
Prove $\left(\frac{a+b+c}{3}\right)^p\leq \frac{a^p+b^p+c^p}{3}$.
Mar 21, 2022
question
1
Prove that $P$ is invertible.
Apr 1, 2022
question
1
Prove $D=${$x\in B:x\cap y=x$ for any $y\in A$} is the empty set
Apr 11, 2022
question
1
Prove $\sum_{j=1}^{n^2} \log_n(2j-1)\leq2n^2 $
Apr 11, 2022
question
1
Prove $[0,1)$ is of cardinality equal to $(0,1]$
Apr 18, 2022
question
1
Prove $a^{1/k}+b^{1/k}\gt (a+b)^{1/k}$ [closed]
May 5, 2022
question
0
Prove that $yz+zx+xy\leq (y+z-x)^2+(z+x-y)^2+(x+y-z)^2$.
Mar 27, 2022
question
0
Prove For any $k\in \Bbb R,$for any $n\in \Bbb N$ \ {$0$} ,there exists some $z\in \Bbb C$ such that $k^2+n\lt |z|$.
Apr 9, 2022

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