证明：3整除n(n+1)(2n+1),其中n是任何整数

下列级数绝对收敛的是()A.sum _(n=1)^infty dfrac ({(-1))^n+1}(2n+1)B.sum _(n=1)^infty dfrac

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

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

例7 证明： 1^3+2^3+3^3+...+n^3=[(n)/(2)(n+1)]^2.例7 证明：$ 1^{3}+2^{3}+3^{3}+\cdots+n^{

9.(2025·全国一卷·高考真题)设数列(a_{n)}满足a_(1)=3,(a_(n+1))/(n)=(a_(n))/(n+1)+(1)/(n(n+1))(1

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

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}=________;________;

(8)[(-1)^n+1](n+1)/(n)。(8)$\left\{\left[(-1)^{n}+1\right]\frac{n+1}{n}\right\}$。

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