2013-01-19 5页 doc 241KB 15阅读
is_608851
暂无简介
1, <0,或00时, { }是递减数列;当q=1时, { }是常数列;当q<0时, { }是摆动数列; 9.等比数列的前n项和公式: ∴当 时, ① 或 ② 当q=1时, 当已知 , q, n 时用公式①;当已知 , q, 时,用公式②. 10. 是等比数列 的前n项和, ①当q=-1且k为偶数时, 不是等比数列. ②当q≠-1或k为奇数时, 仍成等比数列 二、例题讲解 例1 已知等差数列{ }的第二项为8,前十项的和为185,从数列{ }中,依次取出第2项、第4项、第8项、……、第 项按原来的顺序排成一个新数列{ },求数列{ }的通项公式和前项和公式 解:∵ , 解得 =5, d=3, ∴ =3n+2, = =3× +2, =(3×2+2)+ (3× +2)+ (3× +2)+……+(3× +2) =3· +2n=7· -6.(分组求和法) 例2 设数列 为 EMBED Equation.3 求此数列前 项的和 解:(用错项相消法) ① ② ①(② , 当 时, EMBED Equation.3 EMBED Equation.3 当 时, 例3等比数列 前 项和与积分别为S和T,数列 的前 项和为 , 求证: 证:当 时, , , , ∴ ,(成立) 当 时, ∵ , ∴ ,(成立) 综上所述:命题成立 例4设首项为正数的等比数列,它的前 项之和为80,前 项之和为6560,且前 项中数值最大的项为54,求此数列 解:由题意 代入(1), ,得: ,从而 , ∴ 递增,∴前 项中数值最大的项应为第 项 ∴ EMBED Equation.3 EMBED Equation.3 ∴ , ∴ , ∴此数列为 例5求和:(x+ (其中x≠0,x≠1,y≠1) 分析:上面各个括号内的式子均由两项组成,其中各括号内的前一项与后一项分别组成等比数列,分别求出这两个等比数列的和,就能得到所求式子的和. 解:当x≠0,x≠1,y≠1时, (x+ EMBED Equation.3 三、: 设数列 前 项之和为 ,若 且 ,问:数列 成等比数列吗? 解:∵ , ∴ ,即 即: EMBED Equation.3 ,∴ 成等比数列 又: , ∴ 不成等比数列,但当 时成 , 即: 四、小结 本节课学习了以下内容: 熟练求和公式的应用 五、课后作业:课本第68页B组1—3 学习方法报社 第 1 页 共 5 页 _1234567921.unknown _1234567953.unknown _1234567969.unknown _1234567985.unknown _1234567993.unknown _1234567997.unknown _1234568001.unknown _1234568003.unknown _1234568004.unknown _1234568005.unknown _1234568002.unknown _1234567999.unknown _1234568000.unknown _1234567998.unknown _1234567995.unknown _1234567996.unknown _1234567994.unknown _1234567989.unknown _1234567991.unknown _1234567992.unknown _1234567990.unknown _1234567987.unknown _1234567988.unknown _1234567986.unknown _1234567977.unknown _1234567981.unknown _1234567983.unknown _1234567984.unknown _1234567982.unknown _1234567979.unknown _1234567980.unknown _1234567978.unknown _1234567973.unknown _1234567975.unknown _1234567976.unknown _1234567974.unknown _1234567971.unknown _1234567972.unknown _1234567970.unknown _1234567961.unknown _1234567965.unknown _1234567967.unknown _1234567968.unknown _1234567966.unknown _1234567963.unknown _1234567964.unknown _1234567962.unknown _1234567957.unknown _1234567959.unknown _1234567960.unknown _1234567958.unknown _1234567955.unknown _1234567956.unknown _1234567954.unknown _1234567937.unknown _1234567945.unknown _1234567949.unknown _1234567951.unknown _1234567952.unknown _1234567950.unknown _1234567947.unknown _1234567948.unknown _1234567946.unknown _1234567941.unknown _1234567943.unknown _1234567944.unknown _1234567942.unknown _1234567939.unknown _1234567940.unknown _1234567938.unknown _1234567929.unknown _1234567933.unknown _1234567935.unknown _1234567936.unknown _1234567934.unknown _1234567931.unknown _1234567932.unknown _1234567930.unknown _1234567925.unknown _1234567927.unknown _1234567928.unknown _1234567926.unknown _1234567923.unknown _1234567924.unknown _1234567922.unknown _1234567905.unknown _1234567913.unknown _1234567917.unknown _1234567919.unknown _1234567920.unknown _1234567918.unknown _1234567915.unknown _1234567916.unknown _1234567914.unknown _1234567909.unknown _1234567911.unknown _1234567912.unknown _1234567910.unknown _1234567907.unknown _1234567908.unknown _1234567906.unknown _1234567897.unknown _1234567901.unknown _1234567903.unknown _1234567904.unknown _1234567902.unknown _1234567899.unknown _1234567900.unknown _1234567898.unknown _1234567893.unknown _1234567895.unknown _1234567896.unknown _1234567894.unknown _1234567891.unknown _1234567892.unknown _1234567890.unknown