Solve : $y(x+y)^2=9 $ ; $y(x^3-y^3)=7$

Find $ \lim_{n\to\infty}(\sum_{i=0}^{n}\frac{1}{n+i})$

Find the sum : $C^{n}_{1}$ - $\frac{1}{3} \cdot C^{n}_{3}$ + $\frac{1}{9} \cdot C^{n}_{5}$ - $\frac{1}{27} \cdot C^{n}_{9}$ + ...

Find the max and minimum without using dervivate: $\sqrt{x} +4 \cdot \sqrt{\frac{1}{2} - x}$