高三文科數(shù)學(xué)數(shù)列專題練習(xí)

1、1高三文科數(shù)學(xué)數(shù)列專題練習(xí)1.已知數(shù)列????nanN??是等比數(shù)列且13028.naaa???(1)求數(shù)列??na的通項公式(2)求證:11111321?????naaaa?；(3)設(shè)1log22??nnab求數(shù)列??nb的前100項和.1.解：(1)設(shè)等比數(shù)列??na的公比為q.則由等比數(shù)列的通項公式11nnaaq??得3131aaq??2842q???又??022naq???LL分?數(shù)列??na的通項公式是??12223nnna?

2、???分LL.??123231111211111112221222212nnnaaaa?????????????LL??112n??6分LL??111172nn????分QLL??123111118.naaaa??????分LLL????????????2132log21219212112nnnnnbnbbnnb?????????????????由分又常數(shù)數(shù)列是首項為3公差為2的等差數(shù)列11分LLQLL?數(shù)列??nb的前100項和是??

3、100100991003210200122S??????分LL3(1)求證:數(shù)列是等比數(shù)列????????nna231(2)求數(shù)列的前項和.??nbnnS4.解：證法1:∵是關(guān)于的方程N的兩根1?nnaax022???nnbxx?n()∴????????.211nnnnnnaabaa由得nnnaa21?????????????????nnnnaa23123111故數(shù)列是首項為公比為的等比數(shù)列.????????nna23131321??a

4、1?證法2:∵是關(guān)于的方程N的兩根1?nnaax022???nnbxx?n()∴????????.211nnnnnnaabaa∵nnnnnnnnnaaaa2312312231231111?????????????1231231??????????????nnnnaa故數(shù)列是首項為公比為的等比數(shù)列.????????nna23131321??a1?(2)解:由(1)得即.??1131231??????nnna????nnna1231???∴