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我们利用不完全相等的若干个正数的算术平均数与几何平均数之间的不等式 multiply from i=1 to n a_i~(1/n)<1/n sum from i=1 to n a;(1)引进数e_c 数e是作为数列{(1+1/n)~n}的极限而引入的。为了证明所给数列的极限的存在性,只需证明该数列:①单调增加;②有上界。
We use inequalities between the arithmetic mean and the geometric mean of several positive numbers that are not exactly equal. multiply from i=1 to n a_i~(1/n)<1/n sum from i=1 to na; (1 ) The introduced number e_c is introduced as the limit of the sequence {(1+1/n)~n}. In order to prove the existence of the limit of the given sequence, we only need to prove that the sequence: 1 monotonically increases; 2 has an upper bound.