题目内容
计算:
(1)
(2)1+
+
+
…+
.
(1)
| 362+548×361 |
| 362×548-186 |
(2)1+
| 1 |
| 1+2 |
| 1 |
| 1+2+3 |
| 1 |
| 1+2+3+4 |
| 1 |
| 1+2+3+…+100 |
(1)
,
=
,
=
,
=1;
(2)1+
+
+
…+
,
=
+
+
+
+…+
,
=2×(1-
+
-
+
-
+
-
+…+
-
),
=2×(1-
)
=2×
,
=
.
| 362+548×361 |
| 362×548-186 |
=
| 362+548×361 |
| 361×548+548-186 |
=
| 362+548×361 |
| 361×548+362 |
=1;
(2)1+
| 1 |
| 1+2 |
| 1 |
| 1+2+3 |
| 1 |
| 1+2+3+4 |
| 1 |
| 1+2+3+…+100 |
=
| 2 |
| 1×2 |
| 2 |
| 2×3 |
| 2 |
| 3×4 |
| 2 |
| 4×5 |
| 2 |
| 100×101 |
=2×(1-
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 100 |
| 1 |
| 101 |
=2×(1-
| 1 |
| 101 |
=2×
| 100 |
| 101 |
=
| 200 |
| 101 |
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