问题 填空题
(2+
1
2
)+(4+
1
4
)+…+(2n+
1
2n
)
=______.
答案

(2+

1
2
)+(4+
1
4
)+…+(2n+
1
2n
)

=2(1+2+…+n)+(

1
2
+
1
4
+…+
1
2n

=2×

n(n+1)
2
+
1
2
(1-
1
2 n
 )
1-
1
2

=n2+n+1-

1
2n

故答案为:n2+n+1-

1
2n

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