a(n+1)=an²ï¼a1=3
æ以anï¼0
æ
两边å对æ°å¾lna(n+1)=lnan²=2lnan
æ以æ°å{lnan}æ¯
çæ¯æ°åï¼å
¬æ¯æ¯q=2,é¦é¡¹æ¯lna1=ln3
æ以lnan=lna1*2^(n-1)=ln3*2^(n-1)=ln3^[2^(n-1)]
æ
an=3^[2^(n-1)]=9^(n-1)
æ以an=3 (n=1)
=9^(n-1) (nâ¥2)
ä¹æ以è¦åå¼åæ¯å 为a1=3ä¸æ»¡è¶³an=9^(n-1)ãå½ç¶åé¢an=3^[2^(n-1)]ä¸åç®çè¯a1=3ä¹æ»¡è¶³ï¼å°±å¯ä»¥ç»ä¸åãã