已知两等差数列an.bn,且a1+a2+.+an/b1+b2+.+bn=3n+1...
发布网友
发布时间：2024-10-23 07:58
共1个回答
热心网友
时间：2024-11-09 16:05
a₂+
a₃+
a₄+
.+
an]/[b₁+
b₂+
b₃+
b₄+
.+
bn
]=
[(a+an)n/2]/[(b+bn)n/2]=
(a+an)/(b+bn)=
[a+(n-1)A]/[b+(n-1)B]
[a+(n-1)A]/[b+(n-1)B]
=
(3n+1)/(4n+3)当n=1时,a/b
=
4/7,a
=
4b/7当n⟼∞,A/B
=
3/4当n=2时,[a+A]/[b+B]
=
7/1111a
+
11A
=
7b
+
7B11(4b/7)
+
11A
=
7b
+
7(4A/3)44b/7
+
11A
=
7b
+
28A/3A
=
3b/7B
=
4A/3
=
4b/7
=
a所以,an
=
a
+
(n-1)A
=
a
+
(n-1)3b/7
=
a
+
3(n-1)a/4
=
¼(3n+1)a任意给定一个a,即可构成{an}bn
=
b
+
(n-1)
=
7a/4
+
(n-1)B
=
7a/4
+
(n-1)a
=
¼(4n+3)a对应于a,就可以形成一个符合题意的{bn}.
