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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決

Aug 25th 2013, 04:27

觀察下列數列a_1，a_2，a_3，a_4，a_5，a_6，.......如下：
1，10.1，101.01，1010.101，10101.0101，101010.10101，.......
此處一般項a_n用十進制表示時是n個1和(n-1)個0交錯排列，整數部分是n位數。
試求：
(1)用一般式表示a_n
(2)求此數列從首項到第n項的和為何?

煩請給予詳細計算過程，謝謝^0^~~~~

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