数学试题讲解

数列

{a_{n}}

满足

a_{n + 1} + 2 a_{n} a_{n + 1} - a_{n} = 0 (n \in N^{*}), a_{1} = 1

, 则下列结论正确的是

A. 若

b_{n} = 3^{\frac{1}{a_{n}}}

, 则

{b_{n}}

为等比数列 B. 若

c_{n} = \frac{1}{n} (\frac{1}{a_{1}} + \frac{1}{a_{2}} + \dots + \frac{1}{a_{n}})

, 则

{c_{n}}

为等差数列 C.

a_{n} = 2 n - 1

\frac{1}{a_{1}} + \frac{1}{a_{2}} + \dots + \frac{1}{a_{2 n - 1}} = \frac{2 n - 1}{a_{n}}