题目内容
已知ax2+bx+1与2x2-3x+1的积不含x3和x项，试计算下面代数式的值．
+
+
+
+…+
．
| 1 |
| (a-1)(b-1) |
| 1 |
| ab |
| 1 |
| (a+1)(b+1) |
| 1 |
| (a+2)(b+2) |
| 1 |
| (a+2010)(b+2010) |
（ax2+bx+1）•（2x2-3x+1），
=2ax4-3ax3+ax2+2bx3-3bx2+bx+2x2-3x+1，
=2ax4+（-3a+2b）x3+（a-3b+2）x2+（b-3）x+1，
∵不含x3和x项，
∴b-3=0，-3a+2b=0，
∴b=3，a=2，
把a=2，b=3代入得：
+
+
+
+…+
=
+
+
+
+…+
=
-
+
-
+
-
+
-
+…+
-
=1-
=
．
=2ax4-3ax3+ax2+2bx3-3bx2+bx+2x2-3x+1，
=2ax4+（-3a+2b）x3+（a-3b+2）x2+（b-3）x+1，
∵不含x3和x项，
∴b-3=0，-3a+2b=0，
∴b=3，a=2，
把a=2，b=3代入得：
| 1 |
| (a-1)(b-1) |
| 1 |
| ab |
| 1 |
| (a+1)(b+1) |
| 1 |
| (a+2)(b+2) |
| 1 |
| (a+2010)(b+2010) |
=
| 1 |
| 1×2 |
| 1 |
| 2×3 |
| 1 |
| 3×4 |
| 1 |
| 4×5 |
| 1 |
| 2012×2013 |
=
| 1 |
| 1 |
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 2012 |
| 1 |
| 2013 |
=1-
| 1 |
| 2013 |
=
| 2012 |
| 2013 |
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