+(n)^3);-|||-(2) lim _(narrow infty )n[ dfrac (1)({(n+1))^2}+dfrac (1)({(n+2))^2}+... +dfrac (1)({(n+n))^2}] ;-|||-(3) lim _(narrow infty )n(dfrac (1)({n)^2+1}+dfrac (1)({n)^2+(2)^2}+... +dfrac (1)(2{n)^2});-|||-(4) lim _(narrow infty )dfrac (1)(n)(sin dfrac (pi )(n)+sin dfrac (2pi )(n)+... +sin dfrac (n-1)(n)pi )

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

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} ,

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