例7 证明： 1^3+2^3+3^3+...+n^3=[(n)/(2)(n+1)]^2.

lim_(n→∞)(({2^n)+(3^n)})/(({2^n+1)+{3^n+1)}}= ____ ．$\lim_{n→∞}\frac{{{2^n}+{3^n

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

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

7.设-|||-._(1)=2 , _(n+1)=dfrac (1)(2)((x)_(n)+dfrac (2)({x)_(n)}) , n=1 ,2,3,...

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

1.求下列极限:-|||-(1) lim _(narrow infty )dfrac ({n)^3+3(n)^2+1}(4{n)^3+2n+3} =-|||-(

证明：3整除n(n+1)(2n+1),其中n是任何整数证明：3整除,其中n是任何整数

【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} ;