+dfrac (1)(n(n+1)) =-|||-(3) lim _(narrow infty )(dfrac (1)(2)+dfrac (3)({2)^2}+... +dfrac (2n-1)({2)^n}) ;-|||-(5) lim _(narrow infty )(dfrac (1)({n)^2}+dfrac (1)({(n+1))^2}+... +dfrac (1)({(2n))^2}) ;-|||-(2) lim _(narrow infty )(sqrt (2)sqrt [n](2)sqrt (2)... sqrt [2](2)) =-|||-(4) lim _(narrow infty )sqrt [n](1-dfrac {1)(n)} =-|||-(6) lim _(narrow infty )(dfrac (1)(sqrt {{n)^2+1}}+dfrac (1)(sqrt {{n)^2+2}}+... +dfrac (1)(sqrt {{n)^2+n}})-|||-人旦发散数列.证明 {a)_(n)pm (b)_(n)| 是发数数列

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

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

【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} ;