`a) lim ((-1)^{n})/(n(n + 1))` `(1)`
`text{Ta có}`
`+) lim (-1)^{n} = 1`
`+) lim n(n + 1) = lim [n^{2}(1 + 1/n)] = +infty`
`-> (1) = 1/(+\infty) = 0`
`b) lim (sin n)/(n^2 + 1)`
`= lim (1)/(n^2 + 1)` `(text{|sin n| <= 1)`
`= lim` $\dfrac{\dfrac{1}{n^2}}{1 + \dfrac{1}{n^2}}$
`= 0`