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 37 Evaluate $\frac{0!}{4!}+\frac{1!}{5!}+\frac{2!}{6!}+\frac{3!}{7!}+\frac{4!}{8!}+\cdots$ 30 The sum of series with natural logarithm: $\sum_{n=1}^\infty \ln\left(\frac{n(n+2)}{(n+1)^2}\right)$ 28 Evaluate $\sqrt{2} \cdot \sqrt{4}\cdot \sqrt{8}\cdot \dots$ 13 Why is $10^k - 1$ divisible by $9$? 13 If $f:X\rightarrow Y$ and $V\subseteq Y$, does there exist $U\subseteq X$ such that $f(U)=V$?

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 +10 Calculating the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2}\mathrm{d}x$ without using complex analysis +10 Quadratic variation of the sum +35 Dothan's model - expected value of $B_t$ +10 If $\sin^{-1}x + \sin^{-1}y=\sin^{-1}(x \sqrt{1-y^{2}}+ y \sqrt{1-x^{2}})$, then what is the area represented by the locus of point $(x, y)$?

### Questions (2)

 7 Inequality with a rational polynomial 2 How can we find minimum of $f(x,y,z)?$

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