利用极限存在准则证明：limn趋向于无穷,n【1/（n^2+π）+1/（n^2+2π）+...+1/（n^2+nπ)】=1

夹逼准则n^2/（n^2+nπ)>n【1/（n^2+π）+1/（n^2+2π）+...+1/（n^2+nπ)】>n^2/（n^2+π)
n^2/（n^2+nπ)=n^2/（n^2+π)=1（当n趋向∞）

迫敛准则
设 u(n) =n【1/（n^2+π）+1/（n^2+2π）+ ... +1/（n^2+nπ)】
n * n /(n^2+nπ) lim n->∞ n^2 /(n^2+nπ) = lim n->∞ n^2 / (n^2+π) = 1
lim n->∞ u(n)=1

证明：limn【1/（n^2+π）+1/（n^2+2π）+...+1/（n^2+nπ)】limn【(1/n^2+nπ)+(1/n^2+nπ)+.(1/n^2+nπ)】 =limn(n/(n^2+nπ) =limn/n+π) =1所以limn【1/（n^2+π）+1/（n^2+2π）+...+1/（n^2+n...

lim n【1/（n^2+π）+1/（n^2+2π）+...+1/（n^2+nπ)】
=lim 1/（n+π/n）+1/（n+2π/n）+...+1/（n+π)】
=lim n*1/n
=1