新高考數(shù)學(xué)二輪復(fù)習(xí)重難點突破專題12 數(shù)列求和方法之倒序相加法(原卷版)

專題12數(shù)列求和方法之倒序相加法一、單選題1．已知SKIPIF1<0是SKIPIF1<0上的奇函數(shù)，SKIPIF1<0SKIPIF1<0,SKIPIF1<0,則數(shù)列SKIPIF1<0的通項公式為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0是SKIPIF1<0上的奇函數(shù)，SKIPIF1<0，則數(shù)列SKIPIF1<0的通項公式為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知SKIPIF1<0，SKIPIF1<0（SKIPIF1<0），則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．設(shè)n為滿足不等式SKIPIF1<0的最大正整數(shù)，則n的值為（）．A．11 B．10 C．9 D．85．已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，若數(shù)列SKIPIF1<0滿足SKIPIF1<0，則數(shù)列SKIPIF1<0的前10項和為（）A．SKIPIF1<0 B．33 C．SKIPIF1<0 D．346．已知函數(shù)SKIPIF1<0滿足SKIPIF1<0，若數(shù)列SKIPIF1<0滿足SKIPIF1<0SKIPIF1<0，則數(shù)列SKIPIF1<0的前20項和為（）A．100 B．105 C．110 D．1157．已知函數(shù)SKIPIF1<0，設(shè)SKIPIF1<0（SKIPIF1<0），則數(shù)列SKIPIF1<0的前2019項和SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知SKIPIF1<0若等比數(shù)列SKIPIF1<0滿足SKIPIF1<0則SKIPIF1<0（）A．SKIPIF1<0 B．1010 C．2019 D．20209．設(shè)函數(shù)SKIPIF1<0，利用課本（蘇教版必修SKIPIF1<0）中推導(dǎo)等差數(shù)列前SKIPIF1<0項和的方法，求得SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．設(shè)等差數(shù)列SKIPIF1<0的前SKIPIF1<0項和是SKIPIF1<0，已知SKIPIF1<0，則SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知Fx=fx+12?2是R上的奇函數(shù)，A．a(chǎn)n=n B．a(chǎn)n=212．已知函數(shù)SKIPIF1<0，則SKIPIF1<0的值為（）A．4033 B．-4033C．8066 D．-806613．已知SKIPIF1<0為R上的奇函數(shù)，SKIPIF1<0SKIPIF1<0，則數(shù)列SKIPIF1<0的通項公式為A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題14．設(shè)數(shù)列SKIPIF1<0的通項公式為SKIPIF1<0該數(shù)列的前n項和為SKIPIF1<0，則SKIPIF1<0_________.15．已知函數(shù)SKIPIF1<0，SKIPIF1<0，正項等比數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0等于______．16．設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的導(dǎo)數(shù)，SKIPIF1<0是SKIPIF1<0的導(dǎo)數(shù)，若方程SKIPIF1<0有實數(shù)解SKIPIF1<0，則稱點SKIPIF1<0為函數(shù)SKIPIF1<0的“拐點”.已知：任何三次函數(shù)都有拐點，又有對稱中心，且拐點就是對稱中心.設(shè)SKIPIF1<0，數(shù)列SKIPIF1<0的通項公式為SKIPIF1<0，則SKIPIF1<0_______.17．已知SKIPIF1<0，等差數(shù)列SKIPIF1<0的前SKIPIF1<0項和為SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的值為___________.18．設(shè)函數(shù)SKIPIF1<0，數(shù)列SKIPIF1<0滿足SKIPIF1<0，則SKIPIF1<0______.19．若SKIPIF1<0(SKIPIF1<0)，則數(shù)列SKIPIF1<0的通項公式是___________.20．SKIPIF1<0對任意SKIPIF1<0都有SKIPIF1<0.數(shù)列SKIPIF1<0滿足：SKIPIF1<0SKIPIF1<0，則SKIPIF1<0__________.21．函數(shù)SKIPIF1<0，數(shù)列SKIPIF1<0滿足SKIPIF1<0，其前SKIPIF1<0項和為SKIPIF1<0，則SKIPIF1<0_____.22．推導(dǎo)等差數(shù)列求和公式的方法叫做倒序求和法，利用此法可求得SKIPIF1<0__________.23．設(shè)SKIPIF1<0，利用課本中推導(dǎo)等差數(shù)列前n項和的公式的方法，可求得SKIPIF1<0SKIPIF1<0SKIPIF1<0_________．24．已知數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0，若函數(shù)SKIPIF1<0，記SKIPIF1<0，則數(shù)列SKIPIF1<0的前7項和為__________.25．給出定義：對于三次函數(shù)SKIPIF1<0設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0的導(dǎo)數(shù)，SKIPIF1<0是SKIPIF1<0的導(dǎo)數(shù)，若方程SKIPIF1<0有實數(shù)解SKIPIF1<0，則稱點SKIPIF1<0為函數(shù)SKIPIF1<0的“拐點”，經(jīng)過研究發(fā)現(xiàn)：任何一個三次函數(shù)都有“拐點”；任何一個三次函數(shù)都有對稱中心，且“拐點”就是對稱中心.已知函數(shù)SKIPIF1<0.設(shè)SKIPIF1<0SKIPIF1<0.若SKIPIF1<0則SKIPIF1<0__________．三、解答題26．已知數(shù)列SKIPIF1<0的前n項和為SKIPIF1<0．（Ⅰ）若SKIPIF1<0為等差數(shù)列，求證：SKIPIF1<0；（Ⅱ）若SKIPIF1<0，求證：SKIPIF1<0為等差數(shù)列．27．已知函數(shù)SKIPIF1<0，設(shè)數(shù)列SKIPIF1<0滿足SKIPIF1<0，且SKIPIF1<0.（1）求數(shù)列SKIPIF1<0的通項公式；（2）若記SKIPIF1<0，2，3，SKIPIF1<0，SKIPIF1<0，求數(shù)列SKIPIF1<0的前SKIPIF1<0項和SKIPIF1<0.28．已知f(x)＝SKIPIF1<0(x∈R)，P1(x1，y1)，P2(x2，y2)是函數(shù)y＝f(x)的圖像上的兩點，且線段P1P2的中點P的橫坐標(biāo)是SKIPIF1<0.（1）求證：點P的縱坐標(biāo)是定值；（2）若數(shù)列{an}的通項公式是an＝SKIPIF1<0，求數(shù)列{an}的前m項和Sm.29．已知f(x)＝SKIPIF1<0(x∈R)，P1(x1，y1)，P2(x2，y2)是函數(shù)y＝f(x)的圖像上的兩點，且線段P1P2的中點P的橫坐標(biāo)是SKIPIF1<0.（1）求證：點P的縱坐標(biāo)是定值；（2）若數(shù)列{an}的通項公式是an＝SKIPIF1<0