首页 > 1+112+122=______；1+112+122+1+122+132=______；1+112+122+1+122+132+1+132+142=______；由此猜想1+1n2+1(n+1)2=_

1+112+122=______；1+112+122+1+122+132=______；1+112+122+1+122+132+1+132+142=______；由此猜想1+1n2+1(n+1)2=_

题目简介

1+112+122=______；1+112+122+1+122+132=______；1+112+122+1+122+132+1+132+142=______；由此猜想1+1n2+1(n+1)2=_

题目详情

1+
1
12
+
1
22
=______；
1+
1
12
+
1
22
+
1+
1
22
+
1
32
=______；
1+
1
12
+
1
22
+
1+
1
22
+
1
32
+
1+
1
32
+
1
42

=______；由此猜想
1+
1
n2
+
1
(n+1)2
=______；
1+
1
12
+
1
22
+
1+
1
22
+
1
32
+
1+
1
32
+
1
42
+…+
1+
1
20032
+
1
20042
=______．
题型：解答题难度：中档来源：不详

答案

1+class="stub"1
12
+class="stub"1
22
=
class="stub"9
4
=class="stub"3
2
=1class="stub"1
2
；
1+class="stub"1
12
+class="stub"1
22
+
1+class="stub"1
22
+class="stub"1
32
=class="stub"3
2
+
class="stub"49
36
=class="stub"3
2
+class="stub"7
6
=class="stub"16
6
=class="stub"8
3
=2class="stub"2
3
；
1+class="stub"1
12
+class="stub"1
22
+
1+class="stub"1
22
+class="stub"1
32
+
1+class="stub"1
32
+class="stub"1
42
=class="stub"3
2
+class="stub"7
6
+class="stub"13
12
=class="stub"15
4
=3class="stub"3
4
，
猜想：
1+class="stub"1
n2
+class="stub"1
(n+1)2
=1+class="stub"1
n(n+1)
；
1+class="stub"1
12
+class="stub"1
22
+
1+class="stub"1
22
+class="stub"1
32
+
1+class="stub"1
32
+class="stub"1
42
+…+
1+class="stub"1
20032
+class="stub"1
20042
，
=class="stub"3
2
+class="stub"7
6
+class="stub"13
12
+…+（1-class="stub"1
2003×2004
），
=（1+1-class="stub"1
2
）+（1+class="stub"1
2
-class="stub"1
3
）+（1+class="stub"1
3
-class="stub"1
4
）+…+（1+class="stub"1
2003
-class="stub"1
2004
），
=2003+1-class="stub"1
2004
，
=2003class="stub"2003
2004
．
故答案为：1class="stub"1
2
；2class="stub"2
3
；3class="stub"3
4
；1+class="stub"1
n(n+1)
；2003class="stub"2003
2004
．

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