Sn=213+419+6127+…+(2n+13n)=______.-数学

题目简介

Sn=213+419+6127+…+(2n+13n)=______.-数学

题目详情

Sn=2
1
3
+4
1
9
+6
1
27
+…+(2n+
1
3n
)
=______.
题型:填空题难度:偏易来源:不详

答案

Sn=2class="stub"1
3
+4class="stub"1
9
+6class="stub"1
27
+…(2n+class="stub"1
3n
)

=(2+4+6+…+2n)+(class="stub"1
3
+class="stub"1
9
+…+class="stub"1
3n
)

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

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

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

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