an+1^2-a^2=bn an是等差数列 求证bn是等差数列

问题描述:

an+1^2-a^2=bn an是等差数列 求证bn是等差数列

bn=an+1²-an²=(an+1+an)d d为an公差
bn-bn-1=d(an+1+an)-d(an+an-1)=d(an+1-an-1)=d*2d=2d²
得证