若n为正整数,则n~(1/2)+n+1~(1/2)+n+2~(1/2)为无理数.这个命题的证明初看起来似乎简单,但实际上必须分成几步来完成.由于我们只采用反证法,平方和公式,有理数运算及一些公式变形,所用知识没有超出初中阶段,因此这一证明过程的通俗性值得重视.我们依次证明下列4个命题,然后提出几个迄今可能尚无答案的猜测供大家研究.命题1若n为正整数,但非平方数,则n~(1/2)为无理 If n is a positive integer, n ~ (1/2) + n + 1 ~ (1/2) + n + 2 ~ (1/2) is an irrational number. The proof of this proposition may at first seem simple, but in fact Must be divided into several steps to complete.Because we only use the inverse of the law, the square and the formula, the rational number operation and some formula deformation, the knowledge used does not exceed the junior high school, so the proof of the popularity of the process worthy of attention.We have in turn proved the following four propositions, Then we put forward several speculations that may have no answer so far for our research Proposition 1. If n is a positive integer but non-square, n ~ (1/2) is unreasonable