1.要注意层层深入要依据成人学员基础差,但分析能力强的特点,在讲课开始时,起点要低些,然后再层层深入,方可取得好的教学效果。如证明不等式(a_1~m+a_2~m+…a_n~m)/n≥((a_1+a_2+…+a_n)/n)~m,可先从(a~2+b~2)/2≥((a+b)/2)~2证起,然后横向推广,证(a~2+b~2+c~2)/3≥((a+b+c)/3)~2,(a~2+b~2+c~2+d~2)/4≥((a+b+c+d)/4)~2,……,直到证得(a_1~2+a_2~2+…+a_n~2)/n≥((a_1+a_2+…+a_n)/n)~2。再引导学生向纵向推广,证明(a~3+b~3)/2≥((a+b)/2)~3,(a~4+b~4)/2≥((a+b)/2)~4……,(a~n+b~n)/2≥ 1. It should be noted that in-depth students should be based on the poor foundation of the adult students, but with the strong analytical ability, the starting point should be lower at the beginning of the lecture, and then further in-depth, in order to obtain good teaching results. If it is proved that the inequality (a_1~m+a_2~m+...a_n~m)/n≥((a_1+a_2+...+a_n)/n)~m, it can be from (a~2+b~2)/2≥( (a+b)/2)~2 is confirmed, then horizontally promoted. (a~2+b~2+c~2)/3≥((a+b+c)/3)~2,(a ~2+b~2+c~2+d~2)/4≥((a+b+c+d)/4)~2,... until it is certified (a_1~2+a_2~2+... +a_n~2)/n≥((a_1+a_2+...+a_n)/n)~2. Re-direct the students to the vertical promotion and prove that (a~3+b~3)/2≥((a+b)/2)~3,(a~4+b~4)/2≥((a+b) /2)~4......,(a~n+b~n)/2≥