已知等差数列an满足:a3=7,a5+a7=26,令bn=1a2n-1(n∈N*),则数列bn的前n项和Tn=______.-数学

题目简介

已知等差数列an满足:a3=7,a5+a7=26,令bn=1a2n-1(n∈N*),则数列bn的前n项和Tn=______.-数学

题目详情

已知等差数列an满足:a3=7,a5+a7=26,令bn=
1
a2n
-1
(n∈N*)
,则数列bn的前n项和Tn=______.
题型:填空题难度:中档来源:不详

答案

∵等差数列an满足:a3=7,a5+a7=26,
∴a3+a5+a7=33,
∴a5=11
∴d=class="stub"11-7
2
=2
∴an=2n+1,
bn=class="stub"1
an2
-1
=class="stub"1
4n(n+1)

∴4Tn=class="stub"1
1×2
+class="stub"1
2×3
+…+class="stub"1
n(n+1)

=1-class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+…+class="stub"1
n
-class="stub"1
n+1
=class="stub"n
n+1

Tn =class="stub"n
4(n+1)

故答案为:class="stub"n
4(n+1)

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