:已知等差数列{an}的前n项和为Sn,设数列bn=Sn/n,求证{bn}是等差数列 感激ing>..
问题描述:
:已知等差数列{an}的前n项和为Sn,设数列bn=Sn/n,求证{bn}是等差数列 感激ing>..
答
设等差数列{an}的公差为d
根据等差数列求和公式可知,Sn=(a1+an)n/2,因此bn=Sn/n=(a1+an)/2
bn+1-bn=(a1+a(n+1))/2-(a1+an)/2=[a(n+1)-an]/2=d/2,为定值
因此{bn}是等差数列