`text{Câu 1}`
`b) S = sqrt{2}.(1 + 1/2 + 1/4 + 1/8 + ... + 1/(2^n) + ...)`
`= sqrt{2}.(1)/(1 - \frac{1}{2})`
`= 2sqrt{2}`
`text{Câu 2}`
`lim (2n^2 - 3)/(-2n^3 - 4)`
`= lim` $\dfrac{\dfrac{2}{n} - \dfrac{3}{n^3}}{-2 - \dfrac{4}{n^3}}$
`= 0`
`lim (n^3 - 2n)/(5n^2 + n - 3)`
`= lim` $\dfrac{1 - \dfrac{2}{n^2}}{\dfrac{5}{n} + \dfrac{1}{n^2} - \dfrac{3}{n^3}}$
`= (1 - 0)/(0 + 0 - 0)`
`= +infty`
`lim (sqrt{n^2 - 3n + 1} + n)`
`= lim [n(sqrt{1 - \frac{3}{n} + \frac{1}{n^2}} + 1)]`
`= + infty.(1 + 1)`
`= + infty`
`lim (sqrt{n^2 - 3n + 1} - n)`
`= lim` $\dfrac{n^2 - 3n + 1 - n^2}{\sqrt{n^2 - 3n + 1} + n}$
`= lim` $\dfrac{\dfrac{1}{n} - 3}{\sqrt{1 - \dfrac{3}{n} + \dfrac{1}{n^2}} + 1}$
`= (0 - 3)/(1 + 1)`
`= -3/2`
`lim (sqrt{n^2 - 3n + 1} - 2n)`
`= lim [n(sqrt{1 - \frac{3}{n} + \frac{1}{n^2}} - 2)]`
`= + infty.(-1)`
`= - infty`
