Question

若两个等差数列{An}和{Bn}的前n项和分别为An、Bn,且满足An/Bn=(2n+1)/(3n+1),则a10/b10=

Answer 1

∵a10=0.5(a1+a19),b10=0.5(b1+b19)
∴a10/b10=(a1+a19)/(b1+b19)=19(a1+a19)/19(b1+b19)=A19/B19=39/58

Answer 2

An=(2n+1)n Bn=(3n+1)n
An-1=2(n-1)²+n-1 Bn=3(n-1)²+n-1
an=4n-1 bn=6n-2
a10=39 b10=58
39/58

Answer 3

a1+a19=a1+(a1+18d1)=2(a1+9d1)=2a10
a2+a18=(a1+d1)+(a1+17d1)=2(a1+9d1)=2a10
...
A19=a1+a2+a3+...+a19=(a1+a19)+(a2+a18)+....(a9+a11)+a10=19a10
同理
B19=19b10
a10/b10=A19/B19=39/58