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                                                                                                                已知eqIdf458db68122849abb588feb2e682d9ac位数满足下列条件:①各个数字只能从集合eqIdcb213fe5029745a689798a0f14db0753中选取;②若其中有数字4,则在4的前面不含2.将这样的n位数的个数记为eqIdc2aee1ecc2e14b4e93460afefc19026c
                                                                                                                (1)求eqIdb83533b2e4884c51938be9b575d59257
                                                                                                                (2)探究eqId9c34915c981b4f0e8587a8d431f28ad5eqIdef9cef8e6d054d8dac46b8cde14953ad之间的关系,求出数列eqId93e38ecd74a24cb59da79181b95bfd3a的通项公式;
                                                                                                                (3)对于每个正整数eqId4d2187284c5d4de29906363f7d21f60f,在eqId75691f28a5bb4c8287401017aa3a2d29eqIdabb627afd6fa45ca9ac1fdb32c22cc84之间插入eqIdb4dc7e75bde8484ca7e6d63aebee9d25eqIda8012d5322b240128851ebf3cd086e12得到一个新数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63,设eqIddb5481de79c946c0a760143297d5eade是数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63的前eqIdf458db68122849abb588feb2e682d9ac项和,试探究eqIda543d7413bb54b1eaad1b8c82530f160能否成立?写出你探究得到的结论并给出证明.
                                                                                                                更新:2019/12/6难度系数:0.65题型:解答题组卷:0次
                                                                                                                eqIdbb027835f0ad4734b91fb147c268e634,若存在eqId7681b8ede8a348aba1ed17317dc0a48b,使得eqId11014d5235bc4a458a37efd6d6371ee6,且对任意eqIdd0bc797a39da4e228a36b16e73ec423c,均有eqId0bc6e6eab302489a8f0e9e5dff8d6943(即eqId4461be70c0df4caeabc985fa0d8a9eb8是一个公差为eqId096e32e1d18145d199ccbacb5a9a85fe的等差数列),则称数列eqIdb83dce5eaa614e0396991d098bdeaddd是一个长度为eqId3a4208e0040c42ed8b09de2cae9d562e的“弱等差数列”.
                                                                                                                (1)判断下列数列是否为“弱等差数列”,并说明理由.
                                                                                                                ①1,3,5,7,9,11;
                                                                                                                ②2,eqId66c0900a062542efad284436e64c7fa6eqIdee647a68371e409ba932f6b3612c905beqId496bc3d9eb2748e79119c82d7034c348eqId6c88304da6f14643847ebc0dbda9355c.
                                                                                                                (2)证明:若eqIdfa9d603221c445a3b9d62c685ff36534,则数列eqId7ecc97f45f174fd49db1949eb9bdcb51为“弱等差数列”.
                                                                                                                (3)对任意给定的正整数eqIdb7bea8a7cdaf4e88a31a662c11210d18,若eqId911a5b0c38874f28a952ca3a3c011154,是否总存在正整数eqId4d2187284c5d4de29906363f7d21f60f,使得等比数列:eqIdc0c5a7ca69364a8d97578ed57e39e03e是一个长度为eqId3a4208e0040c42ed8b09de2cae9d562e的“弱等差数列”?若存在,给出证明;若不存在,请说明理由
                                                                                                                更新:2019/12/6难度系数:0.15题型:解答题组卷:0次
                                                                                                                过抛物线的一条弦的中点作平行于抛物线对称轴的平行线(或与对称轴重合),交抛物线于一点,称以该点及弦的端点为顶点的三角形为这条弦的阿基米德三角形(简称阿氏三角形).
                                                                                                                现有抛物线eqId2381423d4cd146cab95f55527681a766:eqId43f1d2862e0b4c1abbb67dd000733006,直线eqId417e80f1349244878d01fe90e0891f5feqIde2b4fa745c654bc8909303e15ee07de0(其中eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1是常数,且eqId982da3835b7946d999cc8604a2ece266),直线eqId417e80f1349244878d01fe90e0891f5f交抛物线eqId2381423d4cd146cab95f55527681a766eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,设弦eqId99a3187c2b8f4bcc9703c74c3b72f1f3的阿氏三角形是eqId64b9b599fdb6481e9f8d9a94c102300b.
                                                                                                                figure
                                                                                                                (1)指出抛物线eqId2381423d4cd146cab95f55527681a766的焦点坐标和准线方程;
                                                                                                                (2)求eqId64b9b599fdb6481e9f8d9a94c102300b的面积(用eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqIdad7cefefaba947e1a168bca491c4fca1表示);
                                                                                                                (3)称eqId99a3187c2b8f4bcc9703c74c3b72f1f3的阿氏eqId64b9b599fdb6481e9f8d9a94c102300b为一阶的;eqIdcf2da96900c948a1b3ce7cbfd420c080eqId0627be51821d4be7b3e024a354815d64的阿氏eqId239d8db026dd4c4981bfa8af4cce065beqId17f1a7d90f314522bf04ade3b7bd22ba为二阶的;eqIdbf4db7d066034b139ff80a09ab139d45eqIde3de99d6c54049cc9915165f22199e1feqId5bc8e1134afb4130a2c2d1a5b3e30dd6eqId79458ebbe0e04409b432d43f77370566的阿氏三角形为三阶的;……,由此进行下去,记所有的eqId2745e3f9e2e947a0962a0ece4641e158阶阿氏三角形的面积之和为eqIdd697daf766584285b3a07abeb3439b18,探索eqIdd697daf766584285b3a07abeb3439b18eqId4554e473b3634d4d8704ef23e278b83b之间的关系,并求eqIdde8169ed5f6f4c77b02563c86b6e9d98.
                                                                                                                更新:2019/12/5难度系数:0.4题型:解答题组卷:0次
                                                                                                                如果数列eqId93e38ecd74a24cb59da79181b95bfd3a对任意的eqId532dc4d959024b79b546428f5856e5aa满足:eqId6905f7bf4c1b4718bfb25a2f1465a512,则称数列eqId93e38ecd74a24cb59da79181b95bfd3a为“eqId2381423d4cd146cab95f55527681a766数列”.
                                                                                                                (1)已知数列eqId93e38ecd74a24cb59da79181b95bfd3a是“eqId2381423d4cd146cab95f55527681a766数列”,设eqIdc28a4bba5b0c4038a4fba90830868e45,求证:数列eqIdeeb4ca98872f4e6d91cea28f43fc0b63是递增数列,并指出eqIde447ee4358204d97b0f150198a4ee6deeqId119a390c00364ce6b89a6e0e7a6090b2的大小关系(不需要证明);
                                                                                                                (2)已知数列eqId93e38ecd74a24cb59da79181b95bfd3a是首项为eqId37705e1ef6a84bbdbe88433e75932cdf,公差为eqId2b3ae554ddd1457bb01e7867b5b72ae1的等差数列,eqIddb5481de79c946c0a760143297d5eade是其前eqIdf458db68122849abb588feb2e682d9ac项的和,若数列eqId817dc850f13c457a8972ed434ce71c20是“eqId2381423d4cd146cab95f55527681a766数列”,求eqId096e32e1d18145d199ccbacb5a9a85fe的取值范围;
                                                                                                                (3)已知数列eqId93e38ecd74a24cb59da79181b95bfd3a是各项均为正数的“eqId2381423d4cd146cab95f55527681a766数列”,对于eqIdf458db68122849abb588feb2e682d9ac取相同的正整数时,比较eqId729482c1b6144d63911d56fb93eb62b6eqId0d82703365a140a6a344fd4cc4ac983b的大小,并说明理由.
                                                                                                                更新:2019/12/5难度系数:0.15题型:解答题组卷:0次
                                                                                                                王某2017年12月31日向银行贷款eqId78e35913d69c4a1db4490dc798d9d5ce元,银行贷款年利率为eqId5af2629578db4fa4854fa1a187dcb0d0,若此贷款分十年还清(2027年12月31日还清),每年年底等额还款(每次还款金额相同),设第eqIdf458db68122849abb588feb2e682d9ac年末还款后此人在银行的欠款额为eqIdef9cef8e6d054d8dac46b8cde14953ad元.
                                                                                                                (1)设每年的还款额为eqId3a4208e0040c42ed8b09de2cae9d562e元,请用eqId3a4208e0040c42ed8b09de2cae9d562e表示出eqId0509add794484602a2c710f41d9ddddc
                                                                                                                (2)求每年的还款额(精确到eqId37705e1ef6a84bbdbe88433e75932cdf元).
                                                                                                                更新:2019/12/5难度系数:0.65题型:解答题组卷:0次
                                                                                                                数列eqId93e38ecd74a24cb59da79181b95bfd3a中,若eqIdb5d5624dfe93468ab4dc51abaed2cdb1,则下列命题中真命题个数是(????)
                                                                                                                (1)若数列eqId93e38ecd74a24cb59da79181b95bfd3a为常数数列,则eqId948d8d2aa44241ccbca5ede421a3ecc0
                                                                                                                (2)若eqIdcf0e4bb0507e4f2dbf59a7bdad7cf341,数列eqId93e38ecd74a24cb59da79181b95bfd3a都是单调递增数列;
                                                                                                                (3)若eqId1746f07db9164870ac3852f033669356,任取eqId93e38ecd74a24cb59da79181b95bfd3a中的eqId16fc2c4ac7e940cdad49c4a01d735579eqIdd29065d05dba4730888c33a465c8f0c6构成数列eqId93e38ecd74a24cb59da79181b95bfd3a的子数eqId0d029dfad3e8498fa96f52818f076a14eqId757e1ab7a0724a4d8a6dd6cced7744af),则eqId0d029dfad3e8498fa96f52818f076a14都是单调数列.
                                                                                                                A.eqIda86879ae304449a4a6e6461c485a1f13B.eqId37705e1ef6a84bbdbe88433e75932cdf?个C.eqIdc052ddfbd4524f67a79e0e77c2e5656aD.eqId8898c1dc81824f3098bbeae74e8f11fd
                                                                                                                更新:2019/12/5难度系数:0.15题型:单选题组卷:0次
                                                                                                                对于数列eqId93e38ecd74a24cb59da79181b95bfd3a满足:eqIdab624f7c7681408ca908c51c5d2d1556,其前eqIdf458db68122849abb588feb2e682d9ac项和为eqIddb5481de79c946c0a760143297d5eade记满足条件的所有数列eqId93e38ecd74a24cb59da79181b95bfd3a中,eqId45358fb9692d4cf0aafa1c9b0e540f3a的最大值为eqId70a27b6ddf6b478285353abb3b1f3741,最小值为eqIdaea992e70d4943e49e893817eb885ed7,则eqId9b95de2c62e54f599ac66f8b52442cba___________
                                                                                                                更新:2019/12/5难度系数:0.4题型:填空题组卷:0次
                                                                                                                在我国古代数学著作《孙子算经》中,卷下第二十六题是:今有物,不知其数,三三数之剩二,五五数之剩三,七七数之剩二,问物几何?满足题意的答案可以用数列表示,该数列的通项公式可以表示为eqId38e7aab9632e418f8d07479b236353ec________
                                                                                                                更新:2019/12/5难度系数:0.65题型:填空题组卷:0次
                                                                                                                如图,eqIdbe31cc43e5e04923995edbf8a46eb55b是一块半径为2的半圆形纸板,在eqIdbe31cc43e5e04923995edbf8a46eb55b的左下端剪去一个半径为1的半圆得到图形eqIdbae5032529224bfbb359d2cb586a66c7,在eqIdbae5032529224bfbb359d2cb586a66c7的左下端剪去一个半径为eqId767acf51abfd4d97a757561d1a882151的半圆得到图形eqId88a3529ca9e14a958f44b54ef94dea0d,……然后依次剪去一个更小的半圆(其直径是前一个被剪掉半圆的半径可得图形eqId8bcaa13fe8f948daa9a0cbaeb62c0486,记纸板eqIdb10e0852b5ff41eabe1836f73d97391a的面积为eqIddb5481de79c946c0a760143297d5eade,求:eqId1a6e3204330a4733b1b3c2758113e9db_____________figure
                                                                                                                更新:2019/12/5难度系数:0.65题型:填空题组卷:0次
                                                                                                                对于给定的正整数eqId4d2187284c5d4de29906363f7d21f60f,若无穷数列eqId93e38ecd74a24cb59da79181b95bfd3a对于任意的eqIdfd1fce51eeb5422d8e76dea0e713f33e都满足:eqIda5af4a760d87410da197bd2b8fc7b720,则称数列eqId93e38ecd74a24cb59da79181b95bfd3a,是eqId38b3a0154e744a9caf0d0af26b4162e3数列.
                                                                                                                (1)若eqId0ba2ac7e43a6481d9906d3ab294013ec,判断eqId93e38ecd74a24cb59da79181b95bfd3a是否为eqId2c202df754464c63bdb6b93ffce39fcf数列,说明理由;
                                                                                                                (2)若数列eqId93e38ecd74a24cb59da79181b95bfd3a既是eqId2c202df754464c63bdb6b93ffce39fcf数列又是eqIded9f01af2b174322b7564eeb1b0b69a5数列,求证:数列eqId93e38ecd74a24cb59da79181b95bfd3a是等差数列.
                                                                                                                更新:2019/12/5难度系数:0.4题型:解答题组卷:0次
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