等差数列{an}中,a7=4,a19=2a9,(I)求{an}的通项公式;(II)设bn=1nan,求数列{bn}的前n项和Sn.-数学

题目简介

等差数列{an}中,a7=4,a19=2a9,(I)求{an}的通项公式;(II)设bn=1nan,求数列{bn}的前n项和Sn.-数学

题目详情

等差数列{an}中,a7=4,a19=2a9
(I)求{an}的通项公式;
(II)设bn=
1
nan
,求数列{bn}的前n项和Sn
题型:解答题难度:中档来源:不详

答案

(I)设等差数列{an}的公差为d
∵a7=4,a19=2a9,
a1+6d=4
a1+18d=2(a1+8d)

解得,a1=1,d=class="stub"1
2

an=1+class="stub"1
2
(n-1)
=class="stub"1+n
2

(II)∵bn=class="stub"1
nan
=class="stub"2
n(n+1)
=class="stub"2
n
-class="stub"2
n+1

∴sn=2(1-class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+…+class="stub"1
n
-class="stub"1
n+1
)

=2(1-class="stub"1
n+1
)
=class="stub"2n
n+1

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