Problems(1)
Let n be some positive integer and a1,a2,…,an be real numbers. Denote
S0=i=1∑nai2,S1=i=1∑naiai+1,S2=i=1∑naiai+2,
where an+1=a1 and an+2=a2.1. Show that S0−S1≥0.
2. Show that 3 is the minimum value of C such that for any n and a1,a2,…,an, there holds C(S0−S1)≥S1−S2. inequalitiesAM-GMalgebra