数列{an}满足an=n(n+1)2(n∈N*),则1a1+1a2+…+1a2013等于______.-数学

题目简介

数列{an}满足an=n(n+1)2(n∈N*),则1a1+1a2+…+1a2013等于______.-数学

题目详情

数列{an}满足an=
n(n+1)
2
(n∈N*),则
1
a1
+
1
a2
+…+
1
a2013
等于______.
题型:填空题难度:中档来源:不详

答案

∵an=
n(n+1)
2
(n∈N*),
class="stub"1
an
=2×(class="stub"1
n
-class="stub"1
n+1
),
class="stub"1
a1
+class="stub"1
a2
+…+class="stub"1
a2013

=2[(1-class="stub"1
2
)+(class="stub"1
2
-class="stub"1
3
)+…+(class="stub"1
2013
-class="stub"1
2014
)]
=2(1-class="stub"1
2014

=class="stub"2013
1007

故答案为:class="stub"2013
1007

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