题目内容
计算：(1+| 1 |
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分析：首先可设(1+
+
+…
)=a，(
+
+…+
)=b，可得到a-b=1，再将a、b整体代入代数式求值即可解答．
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解答：解：设(1+
+
+…
)=a，(
+
+…+
)=b，
则a-b=1．
原式=a（b+
）-（a+
）b
=ab+
-ab-
=
=
．
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则a-b=1．
原式=a（b+
| 1 |
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=ab+
| a |
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| b |
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=
| a-b |
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=
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点评：本题主要考查了代数式求值问题．设(1+
+
+…
)=a，(
+
+…+
)=b，然后利用整体代入法代入代数式求值是解答本题的关键．
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