[tex]\left \lceil \frac{3655}{365} \right \rceil=11[/tex]

[tex]\left \lfloor \frac{300}{2} \right \rfloor \left \lfloor \frac{300}{3} \right \rfloor \left \lfloor \frac{300}{5} \right \rfloor-\left \lfloor \frac{300}{6} \right \rfloor-\left \lfloor \frac{300}{10} \right \rfloor-\left \lfloor \frac{300}{15} \right \rfloor \left \lfloor \frac{300}{30} \right \rfloor[/tex]

[tex]=150 100 60-50-30-20 10=220[/tex]

[tex]b_n-2b_{n-1}-2b_{n-2}=0[/tex]

[tex]r^2-2^r-2=0[/tex]

[tex]\Rightarrow r_1=\frac{2 \sqrt{(-2)^2-4\times (-2)}}{2}=1 \sqrt{3}[/tex]

[tex]\Rightarrow r_2=\frac{2-\sqrt{(-2)^2-4\times (-2)}}{2}=1-\sqrt{3}[/tex]

[tex]b_n=a(1 \sqrt{3})^n b(1-\sqrt{3})^n[/tex]

[tex]b_0=a b=0\Rightarrow a=-b[/tex]
[tex]b_1=a b (a-b)\sqrt{3}=1\Rightarrow a=-b=\frac{1}{2\sqrt{3}}[/tex]

[tex]\left\{\begin{matrix} 3r u=29\\ r 2u=18 \end{matrix}\right. \Rightarrow \left\{\begin{matrix} r=8\\ u=5 \end{matrix}\right.[/tex]

[tex]\frac{1}{1-x}=1 x x^2 ...[/tex]
[tex]\Rightarrow x(\frac{1}{1-x})'=\frac{x}{(1-x)^2}=x(1 x x^2 ...)'=x 2x^2 3x^3 4x^4 ...[/tex]
[tex]\Rightarrow x(\frac{x}{(1-x)^2})'=\frac{x(x 1)}{(1-x)^3}=x(x 2x^2 3x^3 ...)'=x 4x^2 9x^3=f(x)[/tex]