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New posts in Alternative Proof
Given a recursion $a_{n+ 1}= \sqrt{na_{n}+ 2n+ 1}$ with $a_{1}\geq 1.$ Prove that $a_{n}\sim n\,{\rm as}\,n\rightarrow\infty$
May 10, 2021
How to find $\operatorname{P.V.}\int_0^1 \frac{1}{x (1-x)}\arctan \left(\frac{8 x^2-4 x^3+14 x-8}{2 x^4-3 x^3-11 x^2+16 x+16}\right) \textrm{d}x$?
May 10, 2021
Why does a convex polyhedron being vertex-, edge-, and face-transitive imply that it is a Platonic solid?
May 10, 2021
An Olympiad geometry question on area lemma.
May 10, 2021
Determinants of matrices defined by the minimum/maximum indices of their entries
May 09, 2021
Is $\sum_{n\ge0}(-1)^n\frac{\Gamma(\tfrac{n+1}{2})}{\Gamma(\tfrac{n}2+1)}=\frac{2}{\sqrt{\pi}}$ true?
May 09, 2021
If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$
May 09, 2021
A tricky inequality: $n(n+1)^{\frac{1}{n}}+(n-2)n^{\frac{1}{n-2}}>2n,\ n\geq3.$
May 09, 2021
Loch Ness monster and Jacob's Ladder Surfaces are NOT homeomorphic
May 09, 2021
Prove $\sum_{m=i}^{n}2^{n-m}\binom{m}{i}=\binom{n+1}{i+1}+\ldots+\binom{n+1}{n+1}=\sum_{m=i}^{n}\binom{n+1}{m+1}$ without induction
May 09, 2021
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