证明：∵122+132+…+1n2＞ 12×3+13×4+…+1n(n+1)=12 −13+13−14+…+1n−1n+1=12−1n+1；又122+132+…+1n2＜11×2+12×3+13×4+…+1(n−1)n=1−12+12−13+14−…+1n−1−1n＜1−1n；所以12−1n+1＜122+1...