数列112,314,518,7116,…,前n项和为()A.n2-12n+1B.n2-12n+1+12C.n2-n-12n+1D.n2-n-12n+1+12-高一数学

题目简介

数列112,314,518,7116,…,前n项和为()A.n2-12n+1B.n2-12n+1+12C.n2-n-12n+1D.n2-n-12n+1+12-高一数学

题目详情

数列1
1
2
,3
1
4
,5
1
8
,7
1
16
,…
,前n项和为(  )
A.n2-
1
2n
+1
B.n2-
1
2n+1
+
1
2
C.n2-n-
1
2n
+1
D.n2-n-
1
2n+1
+
1
2
题型:单选题难度:偏易来源:不详

答案

数列1class="stub"1
2
,3class="stub"1
4
,5class="stub"1
8
,7class="stub"1
16
,…
,的前n项之和
Sn=(1+class="stub"1
2
)+(3+class="stub"1
4
)+(5+class="stub"1
8
)+(7+class="stub"1
16
)+…+
(2n-1+class="stub"1
2n
)

=(1+3+5+…+2n-1)+(class="stub"1
2
+class="stub"1
4
+class="stub"1
8
+…+class="stub"1
2n

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

=n2-class="stub"1
2n
+1

故选A.

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