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在上半年的一次数学课中 ,笔者为学生准备了这样一个题目 :已知列 { an}的递推公式为 an+1 =2 anan +2 ,其中 a1 =2 .(1)求 a2 ,a3 ,a4,a5的值 .(2 )由 (1)猜测数列 { an}的通项公式 ,并证明你的猜测 .笔者的思路是 :由通项公式得出 a2 =1,a3= 23,a4=12 ,a5=25 ,由于从第三项起
In a math lesson in the first half of the year, the author prepared a topic for students: the recurrence formula for the known column {an} is an+1 = 2 anan +2, where a1 = 2 . (1) find a2, a3 , a4, a5 values. (2) From (1) guess the general formula of the series {an} and prove your guess. The author’s idea is: from the general term formula, a2 = 1, a3 = 23, a4 =12, a5=25, as from the third item