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1.xét dãy số $(u_n)$ $u_n=\frac{2n+1}{n^2(n+1)^2}$ $n\in\mathbb{N}$

Tìm lim$(\sum_{n}^{k=1}u_k)$

2. Tính lim$1+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+...+n}$

3. Cho dãy $x_n$$\left\{\begin{matrix} x_1=\frac{3}{2} & & \\ x_n=\sqrt{3x_{n-1}-2} & \forall n\geq 2 & \end{matrix}\right.$

c/n $x_n$ tăng...tìm lim $x_n$

Tìm lim $u_n$ biết

a $u_n=\frac{1}{2\sqrt{1}+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}$

b $u_n=(1-\frac{1}{T_1})\left ( 1-\frac{1}{T_2} \right )...\left ( 1-\frac{1}{T_n} \right )$

với $T_n=\frac{n(n+1)}{2}$

c $u_n=\frac{2^3-1}{2^3+1}.\frac{3^3-1}{3^3+1}.\frac{4^3-1}{4^3+1}...\frac{n^3-1}{n^3+1}$

Cho dãy $u_n$ .....xác định bở...$u_n=\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n}$

tìn lim$S_n=\sum_{k=1}^{n}u_k$

Cho $u_n$ :$\left\{\begin{matrix} u_1=\frac{1}{2} & & \\ u_{n+1}=u_n^2+u_n & & \end{matrix}\right.$

a. CMR $u_n$ tăng và k bị chặn

b. Cho $S_n=\frac{1}{x_1+1}+\frac{1}{x_2+1}+...+\frac{1}{x_n+1}$ tính $limS_n$

GS ĐA THỨC $P(x)=x^n+a_{n-1}x^{n-1}+...+a_1x+1$

với $\mid a_k\mid =1;k=1,2,...,n-1$

có nghiệm thức c/m: $n\leq 3$

Gỉai pt

$\sqrt{13x^2-6x+10}+\sqrt{5x^2-13x+\frac{17}{2}}+\sqrt{17x^2-48x+36}=\frac{1}{2}(36x-8x^2-21)$

$13\sqrt{x^2-x^4}+9\sqrt{x^2+x^4}=16$

$\sqrt{3x^2-1}+\sqrt{x^2-x}-x\sqrt{x^2+1}=\frac{1}{2\sqrt{2}}(7x^2-x+4)$