1 a1a2 , 1 a2a3 ,…, 1 anan+1 是首项为 1 a1a2 = 1 a2q ,公比为 1 q2 ∴ 1 a1a2 + 1 a2a3 +…+ 1 anan+1 = 1 a2q (1? ( 1 q2 )n) 1? 1 q2 = q2n?1 a2q(q2n?q2n?2) 故答案为: q2n?1 a2q(q2n?q2n?2) .