1+1/n+1/n^2+1/n^3+……=1/(1-1/n)怎么推导的?RT1+1/n+1/n^2+1/n^3+……=1/(1-1/n)推导过程

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1+1/n+1/n^2+1/n^3+……=1/(1-1/n)怎么推导的?RT1+1/n+1/n^2+1/n^3+……=1/(1-1/n)推导过程
1+1/n+1/n^2+1/n^3+……=1/(1-1/n)怎么推导的?
RT
1+1/n+1/n^2+1/n^3+……=1/(1-1/n)推导过程

1+1/n+1/n^2+1/n^3+……=1/(1-1/n)怎么推导的?RT1+1/n+1/n^2+1/n^3+……=1/(1-1/n)推导过程
等式左边是首项为1,公比为 1/n 的无穷等比数列的极限和,
利用等比数列求和公式,得左边= (k->∞) lim 1*{ 1 - (1/n)^k } / (1- 1/n) = 1/(1- 1/n)

等比数列求和
1+1/n+1/n^2+1/n^3+...-1/n(1+1/n+1/n^2+1/n^3+...)=1
1+1/n+1/n^2+1/n^3+...=1/(1-1/n)

证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n (1/(n^2 n 1 ) 2/(n^2 n 2) 3/(n^2 n 3) ……n/(n^2 n n)) 当N越于无穷大的极限(1/(n^2+n+1 ) +2/(n^2+n+2) +3/(n^2+n+3) ……n/(n^2+n+n)) 当N越于无穷大的极限 1+(n+2)+(2n+3)+(3n+4)+(4n+5)+……((n-1)n+n)的答案 {[(1+n)(2+n)(3+n)……(n+n)]^(1/n)}/n当趋向正无穷求其极限 e^(1/n)+e^(2/n)+e^(3/n)+…+e^(n-1/n)+e^(n/n)=? 设f(n)=1/n+1+1/n+2+1/n+3+……+1/3n(n∈N+),则f(n+1)-f(n)=? 证明1/(n+1)+1/(n+2)+1/(n+3)+……+1/(n+n) 证明:(3^n)*(2^1/n)>(3^n)+(2^1/n)……n属于正整数 lim(1/n^2+4/n^2+7/n^2+…+3n-1/n^2) VB编程n!+(n+1)!+(n+2)!+(n+3)!+……+(n+m)!要有控件 2^n/n*(n+1) 证明…3整除n(n+1)(n+2) lim(1/n+2/n+3/n+4/n+5/n+……+n/n)=lim(1/n)+lim(2/n)+……+lim(n/n)成立吗?（n趋近于无穷大）为什么不成立? [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简 [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简证明(1/n)^n+(2/n)^n+……+(n-1/n)^n > (n-1)/2(n+1) 对任意n正整数成立化简n分之n-1+n分之n-2+n分之n-3+.+n分之1 化简n分之n-1+n分之n-2+n分之n-3+.+n分之1