数学饭第22餐:数列压轴题放缩技巧(三)
离家出走,数学饭
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本期主打:
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通过数列的递推关系式,探究数列的单调性,有界性,进而改变递推关系式的形式,进行放缩处理. 也就是说,无法直达目标时,可以先试试这个数列具有哪些性质,递推关系式可以有哪些变形,目标的数据有什么特点,自己能不能结合已知,产生一些联想,进而找到它们之间的联系.
波利亚在《怎样解题》中说到:聪明的解题者首先要做的是尽可能充分、清楚地理解题目. 然而光有理解是不够的;他必须全神贯注于题目,他必须热切地期望获得答案. 如果他不能真正唤起解题的欲望,还不如置之不理. 获得真正成功的公开秘密就是要全身心地投入到题目中去.
解题的成功决定于选择正确的角度,决定于从容易接近的一侧来攻克要塞. 为了找出哪一个角度是正确的,哪一侧是容易接近的,我们要尝试各种侧面和角度,我们要变化题目.
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