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

用极限的定义证明lim _(narrow infty )dfrac (sqrt {{n)^2+(a)^2}}(n)=1用极限的定义证明

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

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

+dfrac (1)(sqrt {{n)^2+(n)^2}})= )=______.______.

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

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

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

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