题目内容
请先阅读下列一组内容,然后解答问题:
因为:
=1-
,
=
-
,
=
-
,…,
=
-
,
所以:
+
+
+…+
=(1-
)+(
-
)+(
-
)+…+(
-
)=1-
+
-
+
-
+…+
-
=1-
=
.
计算:(1)
+
+
+…+
(2)
+
+
+…+
.
因为:
1 |
1×2 |
1 |
2 |
1 |
2×3 |
1 |
2 |
1 |
3 |
1 |
3×4 |
1 |
3 |
1 |
4 |
1 |
9×10 |
1 |
9 |
1 |
10 |
所以:
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
9×10 |
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
9 |
1 |
10 |
1 |
10 |
9 |
10 |
计算:(1)
1 |
1×2 |
1 |
2×3 |
1 |
3×4 |
1 |
2013×2014 |
(2)
1 |
1×3 |
1 |
3×5 |
1 |
5×7 |
1 |
49×51 |
(1)原式=1-
+
-
+
-
+…+
-
=1-
=
;
(2)原式=
×(1-
+
-
+
-
+…+
-
)=
.
1 |
2 |
1 |
2 |
1 |
3 |
1 |
3 |
1 |
4 |
1 |
2013 |
1 |
2014 |
1 |
2014 |
2013 |
2014 |
(2)原式=
1 |
2 |
1 |
3 |
1 |
3 |
1 |
5 |
1 |
5 |
1 |
7 |
1 |
49 |
1 |
51 |
25 |
51 |

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