tìm giới hạn:
1) $\mathop {\lim }\limits_{n \to \infty }$ $\frac{1 + \frac{1}{2}+\frac{1}{4}+...+\frac{1}{2^{n}}}{1+\frac{1}{3}+\frac{1}{9}+...+\frac{1}{3^{n}}}$
2) $\mathop {\lim }\limits_{n \to \infty }$ $(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{(n-1).n}$)
3) $\mathop {\lim }\limits_{n \to \infty }$ $\frac{1-2+3-4+...+2n}{\sqrt{n^{2}+1}}$
4) $\mathop {\lim }\limits_{n\to \infty }$ $\left ( 1-\frac{1}{2^{2}} \right ) \left ( 1- \frac{1}{3^{2}} \right )...\left ( 1-\frac{1}{n^{2}} \right ) $