数列113,219,3127,4181,…的前n项和是______.-数学

题目简介

数列113,219,3127,4181,…的前n项和是______.-数学

题目详情

数列1
1
3
,2
1
9
,3
1
27
,4
1
81
,…
的前n项和是 ______.
题型:填空题难度:中档来源:不详

答案

1class="stub"1
3
+2class="stub"1
9
+3class="stub"1
27
+4class="stub"1
81
+nclass="stub"1
3n
=(1+2+3+…+n)+(class="stub"1
3
+class="stub"1
9
+…+class="stub"1
3n

=
n(n+1)
2
+
class="stub"1
3
-class="stub"1
3n+1
1-class="stub"1
3
=
n2+n+1
2
-class="stub"1
2•3n

故答案为:
n2+n+1
2
-class="stub"1
2•3n

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