$\lim _{n \rightarrow \infty} n\left(\frac{1}{1+n^{2}}+\frac{1}{2^{2}+n^{2}}+\cdots+\frac{1}{n^{2}+n^{2}}\right)=$ _____.
lim _(n arrow infty)(1-(1)/(2^2))(1-(1)/(3^2)) ...(1-(1)/(n^2))= ____ $\lim _{n
lim _(narrow infty )(dfrac (1)({n)^2+n+1}+dfrac (2)({n)^2+n+2}+... +dfrac (n)({n
+(n)^3);-|||-(2) lim _(narrow infty )n[ dfrac (1)({(n+1))^2}+dfrac (1)({(n+2))^2
根据数列极限的定义证明：(1) lim_(n to infty) (1)/(n^2) = 0;(2) lim_(n to infty) (3n+1)/(2n+1
+dfrac (1)({2)^n})-|||-1/2^n);(12)-|||-(13) lim _(narrow infty )dfrac ((n+1)(n+2
(2) lim _(narrow infty )dfrac (3{n)^2+n-2}(2{n)^2-n+1}:
12 lim_(n to infty) (1+2+3+...+(n-1))/(n^2);12 $\lim_{n \to \infty} \frac{1+2+3+
lim _(narrow infty )(dfrac (1)({n)^2+(e)^-1+1}+dfrac (2)({n)^2+(e)^-2+2}+dfrac (
59 lim_(n to infty ) sum_(i=1)^n (n)/(n^2)+i^(2+1)=____59 $\lim_{n \to \infty }
lim _(narrow infty )dfrac ({2)^n+(3)^n}({2)^n+1+(3)^n+1}=________;________;