题目
题型:解答题难度:一般来源:不详
1 |
1×2 |
1 |
2 |
1 |
2×3 |
1 |
2 |
1 |
3 |
1 |
3×4 |
1 |
3 |
1 |
4 |
1 |
4×5 |
1 |
4 |
1 |
5 |
(1)则第n个算式为______=______.
(2)如果将上列式子左右相加得:
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
4×5 |
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
5 |
1 |
5 |
4 |
5 |
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
2008×2009 |
②
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
n×(n+1) |
(3)探究并计算
1 |
2 |
1 |
6 |
1 |
12 |
1 |
20 |
1 |
30 |
1 |
42 |
1 |
56 |
1 |
72 |
1 |
90 |
答案
1 |
n(n+1) |
1 |
n |
1 |
n+1 |
(2)①
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
2008×2009 |
=1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
2008 |
1 |
2009 |
=1-
1 |
2009 |
=
2008 |
2009 |
②
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
n×(n+1) |
=1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
n |
1 |
n+1 |
=1-
1 |
n+1 |
=
n |
n+1 |
(3)
1 |
2 |
1 |
6 |
1 |
12 |
1 |
20 |
1 |
30 |
1 |
42 |
1 |
56 |
1 |
72 |
1 |
90 |
=
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
4×5 |
1 |
5×6 |
1 |
6×7 |
1 |
7×8 |
1 |
8×9 |
1 |
9×10 |
=1-
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
=1-
1 |
10 |
=
9 |
10 |
故答案为:
2008 |
2009 |
n |
n+1 |
核心考点
试题【观察下列成立的式子:11×2=1-12,12×3=12-13,13×4=13-14,14×5=14-15…(1)则第n个算式为______=______.(2)】;主要考察你对有理数的混合运算等知识点的理解。[详细]
举一反三