1^2+2^2+…+n^2=n(n+1)(2n+1)/6 原式=lim(n趋近无穷大) n(n+1)(2n+1)/(6n^3)=lim(n趋近无穷大) (n+1)(2n+1)/(6n^2)=lim(n趋近无穷大) 2n^2+3n+1/(6n^2)=1/3