觀察下列計(jì)算:
12+1=2-1(2+1)(2-1)=2-1;
13+2=3-2(3+2)(3-2)=3-2;
14+3=4-3(4+3)(4-3)=4-3;
……
則:
(1)110+9=10-910-9;1100+99=100-99100-99;
(2)從計(jì)算結(jié)果找出規(guī)律; 1n+1+n=n+1-n(n是正整數(shù))1n+1+n=n+1-n(n是正整數(shù));
(3)利用這一規(guī)律計(jì)算:
(12+1+13+2+14+3+?+12024+2023)(2024+1)的值.
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
1
10
+
9
10
9
10
9
1
100
+
99
100
99
100
99
1
n
+
1
+
n
=
n
+
1
-
n
1
n
+
1
+
n
=
n
+
1
-
n
(
1
2
+
1
+
1
3
+
2
+
1
4
+
3
+
?
+
1
2024
+
2023
)
(
2024
+
1
)
【答案】-;-;(n是正整數(shù))
10
9
100
99
1
n
+
1
+
n
=
n
+
1
-
n
【解答】
【點(diǎn)評(píng)】
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發(fā)布:2024/10/16 13:0:2組卷:64引用:2難度:0.5
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