已知两个等差数列{an}与{bn},它的前n项和分别为Sn、S”n,已知Sn/S'n=n+3/n+1...已知两个等差数列{an}与{bn},它的前n项和分别为Sn、S”n,已知Sn/S'n=n+3/n+1则a10/b10=

Question

已知两个等差数列{an}与{bn},它的前n项和分别为Sn、S”n,已知Sn/S'n=n+3/n+1...
已知两个等差数列{an}与{bn},它的前n项和分别为Sn、S”n,已知Sn/S'n=n+3/n+1则a10/b10=

Answer 1

因为两个等差数列{an}与{bn},
所以有Sn/S'n
=(a1+an)/(b1+bn)
=(a2+an-1)/(b2+bn-1)
=...
=（a中间项）/（b中间项）.
于是,S19/S'19=a10/b10.
因为Sn/S'n=n+3/n+1所以S19/S'19=22/20=11/10,
得a10/b10=11/10.