(1)1()+1()=512;(2)1()+1()+1()=1318;(3)12+16+112+120+130+142+156=______;(4)求+10100+10101+10102…+10110

题目简介

(1)1()+1()=512;(2)1()+1()+1()=1318;(3)12+16+112+120+130+142+156=______;(4)求+10100+10101+10102…+10110

题目详情

(1)
1
()
+
1
()
=
5
12

(2)
1
()
+
1
()
+
1
()
=
13
18

(3)
1
2
+
1
6
+
1
12
+
1
20
+
1
30
+
1
42
+
1
56
=______;
(4)求+
10
100
+
10
101
+
10
102
…+
10
110
的整数部分是______.
题型:解答题难度:中档来源:不详

答案

(1)12的因数有:1,2,3,4,6,12,
因2+3=5,所以class="stub"5
12
=class="stub"2
12
+class="stub"3
12
=class="stub"1
6
+class="stub"1
4

因1+4=5,所以class="stub"5
12
=class="stub"1
12
+class="stub"4
12
=class="stub"1
12
+class="stub"1
3


(2)18的因数有:1,2,3,6,9,18,
因13=1+3+9,所以class="stub"13
18
=class="stub"1
18
+class="stub"3
18
+class="stub"9
18
=class="stub"1
18
+class="stub"1
6
+class="stub"1
2


(3)class="stub"1
2
+class="stub"1
6
+class="stub"1
12
+class="stub"1
20
+class="stub"1
30
+class="stub"1
42
+class="stub"1
56

=class="stub"1
2
+(class="stub"1
2
-class="stub"1
3
)+(class="stub"1
3
-class="stub"1
4
)+(class="stub"1
4
-class="stub"1
5
)+(class="stub"1
5
-class="stub"1
6
)+(class="stub"1
6
-
class="stub"1
7
)+(class="stub"1
7
-class="stub"1
8
),
=class="stub"1
2
+class="stub"1
2
-class="stub"1
3
+class="stub"1
3
-class="stub"1
4
+class="stub"1
4
-class="stub"1
5
+class="stub"1
5
-class="stub"1
6
+class="stub"1
6
-class="stub"1
7
+class="stub"1
7
-class="stub"1
8

=1-class="stub"1
8

=class="stub"7
8


(4)class="stub"10
110
×11
class="stub"10
100
+class="stub"10
101
+class="stub"10
102
…+class="stub"10
110
class="stub"10
100
×11

1<class="stub"10
100
+class="stub"10
101
+class="stub"10
102
…+class="stub"10
110
<1.1.
所以它的整数部分是1.
故答案为:6(或12),4(或3),18,6,2,class="stub"7
8
,1.

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