题目内容
计算：
+
+
+…+
．
| 100 |
| 97 |
| 100×99 |
| 97×96 |
| 100×99×98 |
| 97×96×95 |
| 100×99×98×…×5×4 |
| 97×96×95×…×2×1 |
考点：分数的巧算
专题：计算问题（巧算速算）
分析：解：第一项为100×99×98×
第二项为100×99×98×
依此类推，最后一项为 100×99×98×
（总共97项）
现在只需要计算
+…+
=
=
+
-
+…+
=（
+
+…+
）+（
+
+…+
）-（
+
+…+
）
所有
到
的可以全部消掉，得
+
+
+
-
-
=
×（
+
+
-
-
）．
还很难计算．
| 1 |
| 99×98×97 |
第二项为100×99×98×
| 1 |
| 98×97×96 |
依此类推，最后一项为 100×99×98×
| 1 |
| 3×2×1 |
现在只需要计算
| 1 |
| 99×98×97 |
| 1 |
| 3×2×1 |
| 1 |
| 99×98×97 |
| 99×98+97×98-2×99×97 |
| 2×99×98×97 |
| 1 |
| 2×97 |
| 1 |
| 2×99 |
| 1 |
| 98 |
| 1 |
| 99×98×97 |
| 1 |
| 3×2×1 |
| 1 |
| 2×97 |
| 1 |
| 2×96 |
| 1 |
| 2×3 |
| 1 |
| 2×99 |
| 1 |
| 2×98 |
| 1 |
| 2×5 |
| 1 |
| 98 |
| 1 |
| 97 |
| 1 |
| 4 |
所有
| 1 |
| 2×97 |
| 1 |
| 2×5 |
| 1 |
| 2×4 |
| 1 |
| 2×3 |
| 1 |
| 2×99 |
| 1 |
| 2×98 |
| 1 |
| 98 |
| 1 |
| 4 |
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 3 |
| 1 |
| 99 |
| 1 |
| 98 |
| 1 |
| 2 |
还很难计算．
解答：
解：
+
+
+…+
=100×99×98×
+100×99×98×
+…+100×99×98×
=100×99×98×（
+
+…+
）
=100×99×98×（
+…+
）
=100×99×98×[（
+
+…+
）+（
+
+…+
）-（
+
+…+
）]
=100×99×98×[
+
+
+
-
-
]
=100×99×98×
×（
+
+
-
-
）
=100×99×98×
×（
+
-
）
=100×99×98×
×
+100×99×98×
×
-100×99×98×
×
=40425+4900+4950
=50275
| 100 |
| 97 |
| 100×99 |
| 97×96 |
| 100×99×98 |
| 97×96×95 |
| 100×99×98×…×5×4 |
| 97×96×95×…×2×1 |
=100×99×98×
| 1 |
| 99×98×97 |
| 1 |
| 98×97×96 |
| 1 |
| 3×2×1 |
=100×99×98×（
| 1 |
| 99×98×97 |
| 1 |
| 98×97×96 |
| 1 |
| 3×2×1 |
=100×99×98×（
| 1 |
| 99×98×97 |
| 1 |
| 3×2×1 |
=100×99×98×[（
| 1 |
| 2×97 |
| 1 |
| 2×96 |
| 1 |
| 2×3 |
| 1 |
| 2×99 |
| 1 |
| 2×98 |
| 1 |
| 2×5 |
| 1 |
| 98 |
| 1 |
| 97 |
| 1 |
| 4 |
=100×99×98×[
| 1 |
| 2×4 |
| 1 |
| 2×3 |
| 1 |
| 2×99 |
| 1 |
| 2×98 |
| 1 |
| 98 |
| 1 |
| 4 |
=100×99×98×
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 3 |
| 1 |
| 99 |
| 1 |
| 98 |
| 1 |
| 2 |
=100×99×98×
| 1 |
| 2 |
| 1 |
| 12 |
| 1 |
| 99 |
| 1 |
| 98 |
=100×99×98×
| 1 |
| 2 |
| 1 |
| 12 |
| 1 |
| 2 |
| 1 |
| 99 |
| 1 |
| 2 |
| 1 |
| 98 |
=40425+4900+4950
=50275
点评：此题属于较难的计算题目，根据数据特点，找出规律，综合运用运算技巧，灵活简算．
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