(3)收敛, lim _(narrow infty )(2+dfrac (1)({n)^2})=2 --|||-(4)收敛, lim _(narrow infty )dfrac (n-1)(n+1)=1 .-|||-(5) n{(-1))^n} 发散.-|||-(6)收敛, lim _(narrow infty )dfrac ({2)^n-1}({3)^n}=0 --|||-(7) n-dfrac {1)(n)} UNDUND.

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

(6)收敛, lim _(narrow infty )dfrac ({2)^n-1}({3)^n}=0.-|||-(7) n-dfrac {1)(n)} 发

+(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}+

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

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

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

【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} ;