数列{an}满足a1=1,a2=23,且1an+1+1an-1=2an(n≥2),则an=______.-数学

题目简介

数列{an}满足a1=1,a2=23,且1an+1+1an-1=2an(n≥2),则an=______.-数学

题目详情

数列{an}满足a1=1,a2=
2
3
,且
1
an+1
+
1
an-1
=
2
an
(n≥2),则an=______.
题型:填空题难度:中档来源:不详

答案

因为数列{an}满足a1=1,a2=class="stub"2
3
,且class="stub"1
an+1
+class="stub"1
an-1
=class="stub"2
an
(n≥2),
所以数列{ class="stub"1
an
}
是以class="stub"1
a1
=1
为首项,以class="stub"1
a2
-class="stub"1
a1
=class="stub"1
2
为公差的等差数列,
所以class="stub"1
an
=1+(n-1)×class="stub"1
2
=class="stub"n+1
2

所以an=class="stub"2
n+1

故答案为class="stub"2
n+1

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