考虑通式根号(1+1/n^2+1/(n+1)^2)通分 分母是[n（n+1）]^2分子展开 n^4+2n^3+3n^2+2n+1=(n^2+n+1)^2开根号得 （n^2+n+1）/[n（n+1）]=1+1/n-1/(n+1)将每个式子按此方式展开 得到1+1-1/2+1+1/2-1/3.1+1/2010+1/2011=2...