第1个回答 2016-11-10
1平方十2平方十...十n平方证明
答案是:n(n+1)(2n+1)/6 解析:(n+1)^3-n^3=3n^2+3n+1 n^3-(n-1)^3=3(n-1)^2+3(n-1)+1 (n+1)^3-1=3*(1^2+2^2+……+n^2)+3*(1+2+……+n)+n*1 (n+1)^3-1=3*(1^2+2^2+……+n^2)+3*n(n+1)/2+n 1^2+2^2+……+n^2=[(n+1)^3-3n(n+1)/2-(n+1)]/3 =(n+1)(n^2+2n+1-3n/2-1)/3 =(n+1)(2n^2+n)/6 =n(n+1)(2n+1)/6本回答被网友采纳