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当我们面对的是一个较复杂的数学问题时,一个行之有效的办法就是:从原有的问题上退下来看问题。华罗庚教授曾指出:“善于‘退’,‘退”到最原始而不失去重要性的地方,是学好数学的一个诀窍!”一语道出了退一步看问题对数学学习的重要意义。 的确,简单情形象是一把钥匙,一面镜子,可以为我们看清问题助一臂之力。为探索解题途径提供线索和积累经验。 1从简单情形得到解决 例1 等差数列{a_n|中,n≥2,d<0,前n项和是S_n,则有 ( )
When we are faced with a more complex mathematical problem, one effective way is to retreat from the original problem to see the problem. Professor Hua Lugeng pointed out: “Good at ’retreating’ and ’retreating’ to the most primitive place without losing importance is a know-how to learn mathematics!” The phrase reveals a step back to see how important the problem is to mathematics learning. The simple situation is like a key and a mirror, which can help us to see the problem and provide clues and experience for the solution of the problem.1 Solved from a simple case Example 1 In the arithmetic sequence {a_n|, n≥ 2, d<0, the first n items are S_n, and there are ()