题目内容
观察下面的变形规律:
=1-
;
=
-
;
=
-
;…
解答下面的问题:
(1)若n为正整数,请你猜想
=______;
(2)证明你猜想的结论;
(3)求和:
+
+
+…+
.
1 |
1×2 |
1 |
2 |
1 |
2×3 |
1 |
2 |
1 |
3 |
1 |
3×4 |
1 |
3 |
1 |
4 |
解答下面的问题:
(1)若n为正整数,请你猜想
1 |
n(n+1) |
(2)证明你猜想的结论;
(3)求和:
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
2011×2012 |
(1)
=
-
;
(2)
-
=
-
=
=
;
(3)
+
+
+…+
=1-
+
-
+
-
+…+
-
=1-
=
.
1 |
n(n+1) |
1 |
n |
1 |
n+1 |
(2)
1 |
n |
1 |
n+1 |
n+1 |
n(n+1) |
n |
n(n+1) |
n+1-n |
n(n+1) |
1 |
n(n+1) |
(3)
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
2011×2012 |
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
2011 |
1 |
2012 |
1 |
2012 |
2011 |
2012 |
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