摘要：9．已知f (x)＝x+1.g (x)＝2x+1.数列{an}满足:a1＝1.an+1＝则数列{an}的前2007项的和为A．5×22008-2008 B．3×22007-5020 C．6×22006-5020 D．6×21003-5020 [解析]∵a2n+2＝a2n+1+1＝(2a2n+1)+1＝2a2n+2.∴a2n+2+2＝＝2(a2n+2). ∴数列{a2n+2}是以2为公比.以a2＝a1+1＝2为首项的等比数列． ∴a2n+2＝2×2 n-1.∴a2n＝2 n-2． 又a2n+a2n+1＝ a2n+2a2n+1＝3a2n+1.∴数列{an}的前2007项的和为 a1+( a2+ a3)+ ( a4+ a5)+ ( a6+ a7)+ -+ ( a2006+ a2007) ＝ a1+(3a2+1)+ (3a4+1)+ (3a6+1)+ -+ (3a2006+1) ＝ 1++ (3×22-5)+ (3×23-5)+ -+ (3×21003-5) ＝ 1++ (3×22-5)+ (3×23-5)+ -+ (3×21003-5) ＝ 3×(2+22+23+-+21003+1-5×1003 ＝6×(21003-1)+1-5×1003＝6×21003- 5020 .故选D．

网址：http://m.1010jiajiao.com/timu3_id_4459137[举报]