12•4+13•5+14•6+…+1(n+1)(n+3)=______.-数学

题目简介

12•4+13•5+14•6+…+1(n+1)(n+3)=______.-数学

题目详情

1
2•4
+
1
3•5
+
1
4•6
+…+
1
(n+1)(n+3)
=______.
题型:填空题难度:中档来源:不详

答案

数列的通项an=class="stub"1
(n+1)(n+3)
=class="stub"1
2
class="stub"1
n+1
-
class="stub"1
n+3
),
class="stub"1
2•4
+class="stub"1
3•5
+class="stub"1
4•6
+…+class="stub"1
(n+1)(n+3)
=class="stub"1
2
class="stub"1
2
-class="stub"1
4
+class="stub"1
3
-class="stub"1
5
+class="stub"1
4
-class="stub"1
6
+…+class="stub"1
n-1
-class="stub"1
n+1
+class="stub"1
n
-class="stub"1
n+2
+class="stub"1
n+1
-class="stub"1
n+3

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

故答案为:class="stub"1
2
(class="stub"1
2
+class="stub"1
3
-class="stub"1
n+2
-class="stub"1
n+3
)

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