1+2+3+…+n=1/2n(n+1)和1^2+2^+…+n^2=1/6n(n+1)(2n+1)是由什么推导而来的或者是怎么化简的?

证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n 级数n/(n+1)(n+2)(n+3)和是多少 当n为正偶数,求证n/(n-1)+n(n-2)/(n-1)(n-3)+...+n(n-2).2/(n-1)(n-3)...1=n e^(1/n)+e^(2/n)+e^(3/n)+…+e^(n-1/n)+e^(n/n)=? 高数题：n趋近于0,lim｛1/（n^2+n+1)+2/(n^2+n+2)+3/(n^2+n+3)+.+n/(n^2+n+n)｝=? 设f(n)=1/n+1+1/n+2+1/n+3+……+1/3n(n∈N+),则f(n+1)-f(n)=? 为什么:n×(n+1)=1/3[n(n+1)×(n+2)-(n-1)×n×(n+1)] 为什么n(n+1)(n+2)(n+3)=(n²+3n+2)(n²+3n)? 数列a(n)=n (n+1)(n+2)(n+3),求S(n) n+(n+1)+(n+2)+(n+3)+(n+4)=5n+10这道题怎么解 n(n-1)(n-2)（n-3)（n-4)=154440.求N值 要步骤 2^n/n*(n+1) 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 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 f(x)=e^x-x 求证(1/n)^n+(2/n)^n+...+(n/n)^n