Mathematics
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SAINT
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Interesting questions:

How to prove that $1+\frac11(1+\frac12(1+\frac13(...(1+\frac1{n-1}(1+\frac1n))...)))=1+\frac1{1!}+\frac1{2!}+\frac1{3!}+...+\frac1{n!}$?

Positive $x,y,z$, prove $\frac{(x^2+y^2+z^2)^2}{x^3y+y^3z+z^3x} \geq 2 (\frac{xy^2+yz^2+zx^2}{x^2y+y^2z+z^2x})+\frac{x^2y+y^2z+z^2x}{xy^2+yz^2+zx^2}$

Prove that $\frac{x^x}{x+y}+\frac{y^y}{y+z}+\frac{z^z}{z+x} \geqslant \frac32$

How to prove $\sqrt{\frac{ab}{2a^2+bc+ca}}+\sqrt{\frac{bc}{2b^2+ca+ab}}+\sqrt{\frac{ca}{2c^2+ab+bc}}\ge\frac{81}{2}\cdot\frac{abc}{(a+b+c)^3}$

Show that $2 < (1+\frac{1}{n})^{n}< 3$ without using log or binommial coefficient

Is this Batman equation for real?

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