【正文】
na 或 16,3532 ???? nnn bna ( 2)當(dāng) 1?? nn aa 時(shí), ,12 ?? nan )12 112 1(21 )12)(12111????????nnnnaa nn ( 12)1211(21 )12 112 15131311(21??????????????nnnnnT n ? :( 1)∵ 2tan ???ADC ∴55c os,5 52s i n ????? A D CA D C 101055222)55(22 s i n4c o sc o s4s i n )s i n (s i n???????????????A D CA D CA D CC A DA C D?? 在 ACD? 中,由正弦定理得 CA DCDA CDAD ??? s ins in即2210101 CD? 解得 55?CD ( 2)∵ AD∥ BC,∴ ????? 180B C DA D C 5 52s ins in ???? A D CB CD , 55c osc os ????? A D CB CD 在 BCD? 中,由余弦定理得 B C DCDBCBCCDBD ????? c o s2222 即 BCBC 2540 2 ??? 解得 BC=7或 BC=5(舍 ) 75 525721 s in21?????????? B CDCDBCS B C D :( 1)由??? ?? ???? 11 44nnnn aS aS 相減得 nnn aaa ?? ?1 ,即 )2(21 1 ?? ? naa nn 又由 11 4 aS ? 得 21?a 則數(shù)列 }{na 是以21為公比的等比數(shù)列 21 )21(212 ?? ??? nnna )( ( 2) 2)21(loglog 22121 ??? ? na nn 3442 411)41(12)321( )21()21()21(()3201( )()(12222024212312nnnnnnnnnnnbbbbbbT??????????