新高考數(shù)學(xué)二輪復(fù)習(xí)易錯(cuò)點(diǎn)08 數(shù)列（原卷版）

易錯(cuò)點(diǎn)08數(shù)列易錯(cuò)題【01】利用SKIPIF1<0關(guān)系求SKIPIF1<0忽略SKIPIF1<0已知數(shù)列{an}的前n項(xiàng)和Sn,求通項(xiàng)an與Sn的關(guān)系中,an＝Sn－Sn－1,成立的條件是n≥2,求出的an中不一定包括a1,而a1應(yīng)由a1＝S1求出,然后再檢驗(yàn)a1是否在an中,這是一個(gè)典型的易錯(cuò)點(diǎn)．易錯(cuò)題【02】利用等比數(shù)列求和忽略SKIPIF1<0的情況注意等比數(shù)列的求和公式是分段表示的：SKIPIF1<0，所以在利用等比數(shù)列求和公式求和時(shí)要先判斷公比是否可能為1，,若公比未知,則要注意分兩種情況q＝1和q≠1討論.易錯(cuò)題【03】裂項(xiàng)求和剩余項(xiàng)出錯(cuò)用裂項(xiàng)相消法求和時(shí),裂項(xiàng)后可以產(chǎn)生連續(xù)相互抵消的項(xiàng)，但是要注意抵消后并不一定只剩下第一項(xiàng)和最后一項(xiàng),也有可能前面剩兩項(xiàng),后面也剩兩項(xiàng)，一般來說前面剩余幾項(xiàng)后面也剩余幾項(xiàng)，若前面剩余的正數(shù)項(xiàng)，則后面剩余的是負(fù)數(shù)項(xiàng)．易錯(cuò)題【04】混淆數(shù)列與函數(shù)的區(qū)別數(shù)列是一種特殊的函數(shù)，在求解數(shù)列問題時(shí)有時(shí)可以利用函數(shù)的性質(zhì)，但是在利用函數(shù)單調(diào)性求解數(shù)列問題,要注意SKIPIF1<0的取值不是連續(xù)實(shí)數(shù)，忽略這一點(diǎn)很容易出錯(cuò)。 01(2021年高考全國乙卷理科)記SKIPIF1<0為數(shù)列SKIPIF1<0的前n項(xiàng)和，SKIPIF1<0為數(shù)列SKIPIF1<0的前n項(xiàng)積，已知SKIPIF1<0．(1)證明：數(shù)列SKIPIF1<0是等差數(shù)列;(2)求SKIPIF1<0的通項(xiàng)公式．1.(2022屆安徽省六安一中、阜陽一中、合肥八中等校高三上學(xué)期聯(lián)考)數(shù)列SKIPIF1<0中的前n項(xiàng)和SKIPIF1<0，數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，則SKIPIF1<0().A．190 B．192 C．180 D．1822.已知各項(xiàng)均為正數(shù)的數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，其中SKIPIF1<0為常數(shù).(1)證明：SKIPIF1<0；(2)是否存在實(shí)數(shù)SKIPIF1<0，使得數(shù)列SKIPIF1<0為等比數(shù)列？若存在，求出SKIPIF1<0；若不存在，請(qǐng)說明理由. 02【例4】求數(shù)列SKIPIF1<0的前n項(xiàng)和．2．(2022屆遼寧省大連市高三上學(xué)期期中)等比數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0()A．2 B．-2 C．1 D．-12.(2022屆黑龍江省哈爾濱市高三上學(xué)期測試)已知數(shù)列SKIPIF1<0是公比為SKIPIF1<0的等比數(shù)列，SKIPIF1<0是其前SKIPIF1<0和，若SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0 03【例5】求和：SKIPIF1<0________．1．(2022屆廣東省仲元七校高三上學(xué)期11月月考)設(shè)數(shù)列SKIPIF1<0的前n項(xiàng)和SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0成等比數(shù)列.(1)求數(shù)列SKIPIF1<0的通項(xiàng)；(2)數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，求數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0.2.在①SKIPIF1<0，②SKIPIF1<0，③SKIPIF1<0這三個(gè)條件中任選一個(gè)，補(bǔ)充在下面問題中，并解答．已知公差不為0的等差數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，SKIPIF1<0是SKIPIF1<0與SKIPIF1<0的等比中項(xiàng)，______．(1)求SKIPIF1<0的通項(xiàng)公式；(2)若SKIPIF1<0，求數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0．注：如果選擇多個(gè)條件分別解答，按第一個(gè)解答計(jì)分． 04已知SKIPIF1<0,若數(shù)列SKIPIF1<0是遞增數(shù)列,則SKIPIF1<0的取值范圍是.1．(2022屆山東省棗莊市滕州市高三上學(xué)期期中)已知數(shù)列SKIPIF1<0，SKIPIF1<0，則下列說法正確的是()A．此數(shù)列沒有最大項(xiàng) B．此數(shù)列的最大項(xiàng)是SKIPIF1<0C．此數(shù)列沒有最小項(xiàng) D．此數(shù)列的最小項(xiàng)是SKIPIF1<02.(2022屆黑龍江省實(shí)驗(yàn)中學(xué)高三上學(xué)期月考)已知數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，SKIPIF1<0，數(shù)列SKIPIF1<0滿足SKIPIF1<0，SKIPIF1<0．(1)求數(shù)列SKIPIF1<0和SKIPIF1<0的通項(xiàng)公式；(2)設(shè)數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，若不等式SKIPIF1<0恒成立，求實(shí)數(shù)SKIPIF1<0的取值范圍．錯(cuò)1．(2022屆江蘇省徐州市高三上學(xué)期期中)已知等比數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和SKIPIF1<0，數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，若數(shù)列SKIPIF1<0是等差數(shù)列，則非零實(shí)數(shù)SKIPIF1<0的值是()A．SKIPIF1<0 B．SKIPIF1<0 C．3 D．42．(2022屆黑龍江省哈爾濱市高三上學(xué)期期中)數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和為SKIPIF1<0，若SKIPIF1<0，SKIPIF1<0，則()A．?dāng)?shù)列SKIPIF1<0是公比為2的等比數(shù)列 B．SKIPIF1<0C．SKIPIF1<0既無最大值也無最小值 D．SKIPIF1<03．(多選題)()若SKIPIF1<0是公比為SKIPIF1<0的等比數(shù)列，記SKIPIF1<0為SKIPIF1<0的前SKIPIF1<0項(xiàng)和，則下列說法正確的是()A．若SKIPIF1<0，則SKIPIF1<0為遞減數(shù)列B．若SKIPIF1<0，則SKIPIF1<0為遞增數(shù)列C．若SKIPIF1<0，則SKIPIF1<0D．若SKIPIF1<0，則SKIPIF1<0是等比數(shù)列4．(多選題)(2022屆江蘇省新高考基地學(xué)校高三上學(xué)期聯(lián)考)設(shè)數(shù)列SKIPIF1<0的前n項(xiàng)和為SKIPIF1<0，若SKIPIF1<0與SKIPIF1<0的等差中項(xiàng)為常數(shù)t(SKIPIF1<0)，則()A．?dāng)?shù)列SKIPIF1<0是等比數(shù)列B．SKIPIF1<0C．?dāng)?shù)列SKIPIF1<0是遞增數(shù)列D．當(dāng)且僅當(dāng)t<0時(shí)，數(shù)列{(n+1)SKIPIF1<0}是遞增數(shù)列5．(多選題)數(shù)列{an}的前n項(xiàng)和為Sn，SKIPIF1<0，則有()A．Sn＝3n－1 B．{Sn}為等比數(shù)列C．a(chǎn)n＝2·3n－1 D．SKIPIF1<06．(多選題)(2022屆山東省聊城市高三上學(xué)期期中)已知等差數(shù)列SKIPIF1<0的公差為d，前n項(xiàng)和為SKIPIF1<0，若SKIPIF1<0，則下列說法中正確的有()A．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0B．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0取得最大值C．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0D．當(dāng)SKIPIF1<0時(shí)，SKIPIF1<07．(2022屆上海市建平中學(xué)高三上學(xué)期月考)已知SKIPIF1<0，滿足對(duì)于任意的SKIPIF1<0，都有SKIPIF1<0，設(shè)SKIPIF1<0，若對(duì)于任意的SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是______．8.已知正項(xiàng)數(shù)列{an}的前n項(xiàng)和為Sn，?n∈N*,2Sn＝aeq\o\al(2,n)＋an.令bn＝eq\f(1,an\r(an＋1)＋an＋1\r(an))，設(shè){bn}的前n項(xiàng)和為Tn，則在T1，T2，T3，…，T100中有理數(shù)的個(gè)數(shù)為________．9．(2022屆四川省雅安市高三學(xué)業(yè)質(zhì)量監(jiān)測)已知數(shù)列SKIPIF1<0的前SKIPIF1<0項(xiàng)和是SKIPIF1<0，且SKIPIF1<0，等差數(shù)列SKIPIF1<0中，SKIPIF1<0．(1)求數(shù)列SKIPIF1<0的通項(xiàng)公式SKIPIF1<0；(2)定義：SKIPIF1<0記SKIPIF1<0，