lim _(narrow infty )(dfrac (1)({n)^2+n+1}+dfrac (2)({n)^2+n+2}+... +dfrac (n)({n)^2+n+n})=

+(n)^3);-|||-(2) lim _(narrow infty )n[ dfrac (1)({(n+1))^2}+dfrac (1)({(n+2))^2

(4) lim _(narrow infty )((1+dfrac {2)(n)+dfrac (2)({n)^2})}^n.

2.按 -N 定义证明:-|||-(1) lim _(narrow infty )dfrac (n)(n+1)=1 ;-|||-(2) lim _(narrow

+dfrac (n)({n)^2+n+n})=dfrac (1)(2)证明：

+dfrac (1)(n(n+1)) =-|||-(3) lim _(narrow infty )(dfrac (1)(2)+dfrac (3)({2)^2}+

+dfrac (1)({2)^n})-|||-1/2^n);(12)-|||-(13) lim _(narrow infty )dfrac ((n+1)(n+2

lim _(narrow infty )(dfrac (1)({n)^2+(e)^-1+1}+dfrac (2)({n)^2+(e)^-2+2}+dfrac (

(2) lim _(narrow infty )dfrac (3{n)^2+n-2}(2{n)^2-n+1}:

(3)收敛, lim _(narrow infty )(2+dfrac (1)({n)^2})=2 --|||-(4)收敛, lim _(narrow inft

(2) lim _(narrow infty )dfrac (3n+1)(2n+1)=dfrac (3)(2) ;