当n→无穷,求[1+n+(n^2)/2!+...+(n^n)/n!]e^（-n）的极限?分别用高数和概率论的知识来求.主要想知道用概率论怎么来解

(5^n+(-2)^n)/(5^(n+1)+(-2)^(n+1))当n趋近无穷,求极限. 当n趋向于无穷时,求n^(1/2)*[n^(1/n)-1]的极限 求limn→无穷(1+2^n+3^n+4^n+5^n)^1/n 求极限：当n→无穷,1/（n2+n+1）+2/（n2+n+2）+……+n/（n2+n+n）等于?注：n2=n的平方求极限：当n→无穷,1/（n2+n+1）+2/（n2+n+2）+……+n/（n2+n+n）等于?注：n2=n的平方 求当N趋于无穷时,极限N+1/2N-3是多少如题 求极限：lim(x→无穷)(2^n-7^n)/(2^n+7^n-1)=? 当n趋于无穷时,求[sin(π/n)/(n+1)+sin(2π/n)/(n+1/2)+.sinπ/(n+1/n)]的极限 求√n(√(n+2)-√（n+1）),n→无穷,极限, {[(1+n)(2+n)(3+n)……(n+n)]^(1/n)}/n当趋向正无穷 求其极限 当n趋向于无穷时,求极限n[ln(2n)-ln(2n-1)],提示利用等价无穷小. 求极限 n趋向无穷 2^n+1 + 3^n+1/2^n+3^n lim(n/(n^2+1)+...+n/(n^2+n))x趋向于无穷 求解答过程~ 求 证Lim ( n/ n2+1) + (n/ n2+2) +( n/ n2+3).+(n/n2+n)当n趋向无穷时的极限为1 当n趋向无穷时,1/(n^2+1)+2/(n^2+2)+.+n/(n^2+n)的极限是多少 ln(2n^2-n+1)-2ln n.当n趋于正无穷是的极限 (2^n+4^n+6^n+8^n)^(1/n)当n趋于无穷时的极限 当n→无穷,求[1+n+(n^2)/2!+...+(n^n)/n!]e^（-n）的极限?分别用高数和概率论的知识来求.主要想知道用概率论怎么来解 (n-1/n+3)的2n次方当n趋于无穷时的极限