函数f(x)=lnx在x=n(n∈N*)处的切线斜率为an,则a1a2+a2a3+a3a4+…+a2010a2011=______.-数学

题目简介

函数f(x)=lnx在x=n(n∈N*)处的切线斜率为an,则a1a2+a2a3+a3a4+…+a2010a2011=______.-数学

题目详情

函数f(x)=lnx在x=n(n∈N*)处的切线斜率为an,则a1a2+a2a3+a3a4+…+a2010a2011=______.
题型:填空题难度:中档来源:蓝山县模拟

答案

f(x)=class="stub"1
x
,∴an=class="stub"1
n

∴a1a2+a2a3+a3a4+…+a2010a2011=class="stub"1
1
×class="stub"1
2
+class="stub"1
2
×class="stub"1
3
+class="stub"1
3
×class="stub"1
4
+…+class="stub"1
2010
×class="stub"1
2011

=1-class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+class="stub"1
3
-class="stub"1
4
+…+class="stub"1
2010
-class="stub"1
2011

=1-class="stub"1
2011
=class="stub"2010
2011

故答案:class="stub"2010
2011

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