问题
解答题
=______;由此猜想
|
答案
=1+
+1 12 1 22
=9 4
=13 2
;1 2
+1+
+1 12 1 22
=1+
+1 22 1 32
+3 2
=49 36
+3 2
=7 6
=16 6
=28 3
;2 3
+1+
+1 12 1 22
+1+
+1 22 1 32
=1+
+1 32 1 42
+3 2
+7 6
=13 12
=315 4
,3 4
猜想:
=1+1+
+1 n2 1 (n+1)2
;1 n(n+1)
+1+
+1 12 1 22
+1+
+1 22 1 32
+…+1+
+1 32 1 42
,1+
+1 20032 1 20042
=
+3 2
+7 6
+…+(1-13 12
),1 2003×2004
=(1+1-
)+(1+1 2
-1 2
)+(1+1 3
-1 3
)+…+(1+1 4
-1 2003
),1 2004
=2003+1-
,1 2004
=2003
.2003 2004
故答案为:1
;21 2
;32 3
;1+3 4
;20031 n(n+1)
.2003 2004