已知Sn=11×2+12×3+13×4+…+1n×(n+1)(n∈N*)的值是20082009,则n=______.-数学

题目简介

已知Sn=11×2+12×3+13×4+…+1n×(n+1)(n∈N*)的值是20082009,则n=______.-数学

题目详情

已知Sn=
1
1×2
+
1
2×3
+
1
3×4
+…+
1
n×(n+1)
(n∈N*)的值是
2008
2009
,则n=______.
题型:填空题难度:中档来源:不详

答案

∵Sn=class="stub"1
1×2
+class="stub"1
2×3
+class="stub"1
3×4
+…+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

=1-class="stub"1
n+1
=class="stub"n
n+1

class="stub"n
n+1
=class="stub"2008
2009

∴n=2008
故答案为:2008

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