根据数列极限定义证明:(1) lim _(narrow infty )dfrac (1)({n)^2}=0-|||-(2) lim _(narrow infty
+(n)^3);-|||-(2) lim _(narrow infty )n[ dfrac (1)({(n+1))^2}+dfrac (1)({(n+2))^2
+dfrac (1)(n(n+1)) =-|||-(3) lim _(narrow infty )(dfrac (1)(2)+dfrac (3)({2)^2}+
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
(2) lim _(narrow infty )dfrac (3n+1)(2n+1)=dfrac (3)(2) ;
1.利用数列极限的" -N 定义证明:-|||-(1) lim _(narrow infty )dfrac (1)({n)^2}=0;-|||-(2) lim
lim _(narrow infty )(dfrac (1)({n)^2+n+1}+dfrac (2)({n)^2+n+2}+... +dfrac (n)({n
(6)收敛, lim _(narrow infty )dfrac ({2)^n-1}({3)^n}=0.-|||-(7) n-dfrac {1)(n)} 发
(4) lim _(narrow infty )((1+dfrac {2)(n)+dfrac (2)({n)^2})}^n.