观察式子11×3=12(1-13),13×5=13(13-15),15×7=12(15-17),…由此可知11×3+13×5+15×7+…+1(2n-1)×(2n+1)=______.-数学

题目简介

观察式子11×3=12(1-13),13×5=13(13-15),15×7=12(15-17),…由此可知11×3+13×5+15×7+…+1(2n-1)×(2n+1)=______.-数学

题目详情

观察式子
1
1×3
=
1
2
(1-
1
3
)
1
3×5
=
1
3
(
1
3
-
1
5
)
1
5×7
=
1
2
(
1
5
-
1
7
)
,…由此可知
1
1×3
+
1
3×5
+
1
5×7
+…+
1
(2n-1)×(2n+1)
=______.
题型:填空题难度:中档来源:不详

答案

原式=class="stub"1
2
(1-class="stub"1
3
)+class="stub"1
2
class="stub"1
3
-class="stub"1
5
)+…+class="stub"1
2
class="stub"1
2n-1
-class="stub"1
2n+1

=class="stub"1
2
(1-class="stub"1
3
+class="stub"1
3
-class="stub"1
5
+…+class="stub"1
2n-1
-class="stub"1
2n+1

=class="stub"1
2
(1-class="stub"1
2n+1

=class="stub"1
2
×class="stub"2n
2n+1

=class="stub"n
2n+1

故答案为class="stub"n
2n+1

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