问题 解答题
观察下列等式:
1
2
+1
=
2
-1
(
2
+1)(
2
-1)
=
2
-1

1
3
+
2
=
3
-
2
(
3
+
2
)(
3
-
2
)
=
3
-
2

1
4
+
3
=
4
-
3
(
4
+
3
)(
4
-
3
)
=
4
-
3
;…
回答下列问题:
(1)利用你观察到的规律,化简:
1
2
3
+
11

(2)计算:
1
1+
2
+
1
2
+
3
+
1
3
+2
+…+
1
3+
10
答案

(1)原式=

2
3
-
11
(2
3
+
11
)(2
3
-
11
)
=2
3
-
11

(2)原式=

2
-1+
3
-
2
+2-
3
+…+
10
-3
=
10
-1.

实验题