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《中学数学教学》1993年第5期的有奖解题擂台上刊出了下题:“已知正数列{a_n}前n项的和S_n与其通项a_n之间满足S_n·a_n=1/4~n,试求通项a_n的表达式”。本文拟给出该题的解答,并以此说明合理的猜想、严密的证明、丰富的联想、适当的转化对于数学问题的解决,是十分重要的。 解答分三步:1.由题意a_n>0（下文不再重复说
In the “Middle School Mathematics Teaching” 1993 issue of the 5th issue, the following questions were published: “The known positive number column {a_n} before the n term and S_n and its general term a_n satisfy S_n·a_n=1/4 ~n, try the expression for the general term a_n.” This article is intended to give an answer to this question, and it is very important to explain reasonable guesses, rigorous proofs, rich associations, and appropriate transformations to solve mathematical problems. The answer is divided into three steps: 1. The meaning of the question a_n> 0 (will not repeat below