2.按 -N 定义证明:-|||-(1) lim _(narrow infty )dfrac (n)(n+1)=1 ;-|||-(2) lim _(narrow infty )dfrac (3{n)^2+n}(2{n)^2-1}=dfrac (3)(2) ;-|||-(3) lim _(narrow infty )(n)^n=0 ;-|||-(4) lim _(narrow infty )sin dfrac (pi )(n)=0 ;-|||-(5) lim _(narrow infty )dfrac (n)({a)^n}=0(agt 1).

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

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

根据数列极限定义证明：(1) lim _(narrow infty )dfrac (1)({n)^2}=0-|||-(2) lim _(narrow infty

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

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

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

【题文】lim _(narrow infty )dfrac ({2)^n+1+(3)^n+1}({2)^n+(3)^n}=________.【题文】______

[题目]-|||-(5) lim _(narrow infty )dfrac ({(-2))^n+(3)^n}({(-2))^n+1+(3)^n+1} ;

[题目]-|||-(5) lim _(narrow infty )dfrac ({(-2))^n+(3)^n}({(-2))^n+1+(3)^n+1} ;