underset(lim)(n→∞)（1+(1)/(3)+(1)/(9)+…+(1)/((3)^n)）

14.填空题lim_(ntoinfty)(1+(1)/(3)+(1)/(9)+...+(1)/(3^n))=_14.填空题$\lim_{n\to\infty}(

underset(lim)(n→∞)（14n+2(}^{^3n)+32n+4n）{}^(1)/(n)= ____ ．$\underset{lim}{n→∞}$（

5.求极限lim_(ntoinfty)(1+(1)/(n^2))(1+(2)/(n^2))...(1+(n)/(n^2)).5.求极限$\lim_{n\to\i

计算：underset(lim)(n→∞)(1)/(n)[sin(π)/(n)+sin(2π)/(n)+…+sin(（n-1）π)/(n)]．计算：$\unde

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

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

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

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

求underset(lim)(x→1)（(1)/(1-x)-(3)/(1-(x)^3)）求$\underset{lim}{x→1}$（$\frac{1}{1-x

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