问题
解答题
观察下列计算:
则: (1)
(2)从计算结果找出规律:______; (3)利用这一规律计算: (
|
答案
(1)1
+10 9
=
-10 9 (
+10
)(9
-10
)9
=
-10 9 10-9
=
-10
;9
1
+100 99
=
-100 99 (
+100
)(99
-100
)99
=
-100 99 100-99
=
-100
.99
(2)
=1
+n+1 n
-n+1
(n是正整数)n
(3)(
+1
+12
+1
+3 2
+…+1
+4 3
)(1
+2006 2005
+1)2006
=【(
-1)+(2
-3
)+(2
-4
)+…+(3
-2006
)】(2005
+1)2006
=(
-1+2
-3
+2
-4
+3
-2006
)(2005
+1)2006
=(
-1)(2006
+1)2006
=2006-1
=2005