新高考数学二轮复习重难点突破专题12 数列求和方法之倒序相加法(原卷版)

专题12数列求和方法之倒序相加法一、单选题1．已知SKIPIF1<0是SKIPIF1<0上的奇函数，SKIPIF1<0SKIPIF1<0,SKIPIF1<0,则数列SKIPIF1<0的通项公式为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0是SKIPIF1<0上的奇函数，SKIPIF1<0，则数列SKIPIF1<0的通项公式为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知SKIPIF1<0，SKIPIF1<0（SKIPIF1<0），则SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．设n为满足不等式SKIPIF1<0的最大正整数，则n的值为（）．A．11 B．10 C．9 D．85．已知函数SKIPIF1<0满足SKIPIF1<0，若数列SKIPIF1<0满足SKIPIF1<0，则数列SKIPIF1<0的前10项和为（）A．SKIPIF1<0 B．33 C．SKIPIF1<0 D．346．已知函数SKIPIF1<0满足SKIPIF1<0，若数列SKIPIF1<0满足SKIPIF1<0SKIPIF1<0，则数列SKIPIF1<0的前20项和为（）A．100 B．105 C．110 D．1157．已知函数SKIPIF1<0，设SKIPIF1<0（SKIPIF1<0），则数列SKIPIF1<0的前2019项和SKIPIF1<0的值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．已知SKIPIF1<0若等比数列SKIPIF1<0满足SKIPIF1<0则SKIPIF1<0（）A．SKIPIF1<0 B．1010 C．2019 D．20209．设函数SKIPIF1<0，利用课本（苏教版必修SKIPIF1<0）中推导等差数列前SKIPIF1<0项和的方法，求得SKIPIF1<0的值为（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．设等差数列SKIPIF1<0的前SKIPIF1<0项和是SKIPIF1<0，已知SKIPIF1<0，则SKIPIF1<0（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知Fx=fx+12−2是R上的奇函数，A．an=n B．an=212．已知函数SKIPIF1<0，则SKIPIF1<0的值为（）A．4033 B．-4033C．8066 D．-806613．已知SKIPIF1<0为R上的奇函数，SKIPIF1<0SKIPIF1<0，则数列SKIPIF1<0的通项公式为A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空题14．设数列SKIPIF1<0的通项公式为SKIPIF1<0该数列的前n项和为SKIPIF1<0，则SKIPIF1<0_________.15．已知函数SKIPIF1<0，SKIPIF1<0，正项等比数列SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0等于______．16．设SKIPIF1<0是函数SKIPIF1<0的导数，SKIPIF1<0是SKIPIF1<0的导数，若方程SKIPIF1<0有实数解SKIPIF1<0，则称点SKIPIF1<0为函数SKIPIF1<0的“拐点”.已知：任何三次函数都有拐点，又有对称中心，且拐点就是对称中心.设SKIPIF1<0，数列SKIPIF1<0的通项公式为SKIPIF1<0，则SKIPIF1<0_______.17．已知SKIPIF1<0，等差数列SKIPIF1<0的前SKIPIF1<0项和为SKIPIF1<0，且SKIPIF1<0，则SKIPIF1<0的值为___________.18．设函数SKIPIF1<0，数列SKIPIF1<0满足SKIPIF1<0，则SKIPIF1<0______.19．若SKIPIF1<0(SKIPIF1<0)，则数列SKIPIF1<0的通项公式是___________.20．SKIPIF1<0对任意SKIPIF1<0都有SKIPIF1<0.数列SKIPIF1<0满足：SKIPIF1<0SKIPIF1<0，则SKIPIF1<0__________.21．函数SKIPIF1<0，数列SKIPIF1<0满足SKIPIF1<0，其前SKIPIF1<0项和为SKIPIF1<0，则SKIPIF1<0_____.22．推导等差数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．设SKIPIF1<0，利用课本中推导等差数列前n项和的公式的方法，可求得SKIPIF1<0SKIPIF1<0SKIPIF1<0_________．24．已知数列SKIPIF1<0满足SKIPIF1<0，且SKIPIF1<0，若函数SKIPIF1<0，记SKIPIF1<0，则数列SKIPIF1<0的前7项和为__________.25．给出定义：对于三次函数SKIPIF1<0设SKIPIF1<0是函数SKIPIF1<0的导数，SKIPIF1<0是SKIPIF1<0的导数，若方程SKIPIF1<0有实数解SKIPIF1<0，则称点SKIPIF1<0为函数SKIPIF1<0的“拐点”，经过研究发现：任何一个三次函数都有“拐点”；任何一个三次函数都有对称中心，且“拐点”就是对称中心.已知函数SKIPIF1<0.设SKIPIF1<0SKIPIF1<0.若SKIPIF1<0则SKIPIF1<0__________．三、解答题26．已知数列SKIPIF1<0的前n项和为SKIPIF1<0．（Ⅰ）若SKIPIF1<0为等差数列，求证：SKIPIF1<0；（Ⅱ）若SKIPIF1<0，求证：SKIPIF1<0为等差数列．27．已知函数SKIPIF1<0，设数列SKIPIF1<0满足SKIPIF1<0，且SKIPIF1<0.（1）求数列SKIPIF1<0的通项公式；（2）若记SKIPIF1<0，2，3，SKIPIF1<0，SKIPIF1<0，求数列SKIPIF1<0的前SKIPIF1<0项和SKIPIF1<0.28．已知f(x)＝SKIPIF1<0(x∈R)，P1(x1，y1)，P2(x2，y2)是函数y＝f(x)的图像上的两点，且线段P1P2的中点P的横坐标是SKIPIF1<0.（1）求证：点P的纵坐标是定值；（2）若数列{an}的通项公式是an＝SKIPIF1<0，求数列{an}的前m项和Sm.29．已知f(x)＝SKIPIF1<0(x∈R)，P1(x1，y1)，P2(x2，y2)是函数y＝f(x)的图像上的两点，且线段P1P2的中点P的横坐标是SKIPIF1<0.（1）求证：点P的纵坐标是定值；（2）若数列{an}的通项公式是an＝SKIPIF1<0