阿Q吧 > 已知等差数列{an}中,公差d>0,其前n项和为Sn,且满足:a2*a3=45,a1+a4=14

已知等差数列{an}中,公差d>0,其前n项和为Sn,且满足:a2*a3=45,a1+a4=14

2025-06-22 14:20:31

推荐回答（1个）

回答1：

1、
略

2、
a(n+1)=4n+1
bn=1/4*4/(4n-3)(4n+1)
=1/4*[(4n+1)-(4n-3)]/[(4n-3)(4n+1)]
=1/4*{(4n+1)/[(4n-3)(4n+1)]-(4n-3)/[(4n-3)(4n+1)]}
=1/4*[1/(4n-3)-1/(4n+1)]
所以Sn=1/4*[1/1-1/5+1/5-1/9+1/9-1/13+……+1/(4n-3)-1/(4n+1)]
==1/4*[1-1/(4n+1)]
=n/(4n+1)