已知等差数列〔an〕满足a1=1,an+1

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/18 08:35:17
已知等差数列〔an〕满足a1=1,an+1
xP]KA+8hÎGIAlEFAF` RF?ƝU 7BysϹs\ZڠWPA_p Qf # .1񶶝N.-va#*(s"[3T &6.vm8&K x,P6Y`̸KRg$ILI* .W4tLO7$hhXT׮m{lJc=Ap&x9;9.qij;wTEaB7A&o"(JAb%5˲̮eZ \51P4˜78WG[3 %98m{߇A

已知等差数列〔an〕满足a1=1,an+1
已知等差数列〔an〕满足a1=1,an+1

已知等差数列〔an〕满足a1=1,an+1
令公差为d,则a2=d+1,a3=1+2d,所以
(a1+1)(a3+3)=(a2+1)^2
4d+8=d^2+4d+4
d^2=4
又an+11(an*an+1)=(1/an-1/an+1)/d
所以Sn=[(1/a1-1/a2)+(1/a2-1/a3).+(1/an-1/an+1)]/d
=(1/a1-1/an+1)/d
=[1-1/(1-2n)]/d
=n/(1-2n)

令公差为d,则a2=d+1,a3=1+2d,所以
(a1+1)(a3+3)=(a2+1)^2
4d+8=d^2+4d+4
d^2=4
d=正负2
又an+11(an*an+1)=(1/an-1/an+1)/d
所以Sn=[(1/a1-1/a2)+(1/a2-1/a3).......+(1/an-1/an+1)]/d
=(1/a1-1/an+1)/d
=[1-1/(1-2n)]/d
=n/(1-2n)

(2+d)^2=2(4+2d) d<0 d=-2
an=1-2(n-1)=3-2n
1/an =1/(3-2n)
1/an*an+1=1/2(1/an+1-1/an)

此题早几年我会,现在早都还给老师了。

已知等差数列〔an〕满足a1=1,an+1 已知数列an满足 a1=1/2,an+1=3an/an+3求证1/an为等差数列已知数列an满足 a1=1/2,an+1=3an/an+3求证1/an为等差数列 已知数列{An}满足A1=1,An+1=2An+2^n.求证数列An/2是等差数列 已知数列[an]满足An+1=1+an /3-an ,且a1=1/3,求证数列[1/(an -1)]是等差数列,并求an 已知数列{an}满足2an/an+2=an+1(n属于正整数),a1=1/1006.求证:数列{1/an}是等差数列,并求通项an 已知数列{an}满足a1=2,an+1=2an/an+2.求证数列{1/an}是否为等差数列 并求出an 已知等差数列{an}满足a(n+1)=an+3n+2,且a1=2,求an.雪地跪拜! 已知等差数列{an}中,a1=2.an+1=an+3分之an 求an 已知递增的等差数列{An}满足A1=1且A1,A2,A5成等比数列.(1)求等差数列{An}的通项An 已知数列{an},{bn}满足a1=2,2an=1+2an*an+1,设{bn}=an-1求数列{1n}为等差数列急!!! 已知an满足a1=三分之二 an+1=an-2/2an-3 求证1/an-1是等差数列如题 已知数列an满足an+1=3an/an+3求证{1/an}是等差数列.当a1=1/2时求a100 已知数列an满足:an+1-2an=2^n+1,且a1=2 (1)证明{an/2^n}是等差数列 (2)求数列an的 已知数列an满足a1=3,An+1=2An+2^n (1)求证数列[An/2^n]是等差数列 (2)求an通项公式 已知数列{an}满足an+1=(3an+1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an题目错了……重发已知数列{an}满足an+1=(an-1)/(an+3),a1=-1/3 求证1/(an)+1为等差数列,求an 已知数列{an}满足a1=1 an+1=an/(3an+1) 则球an 已知数列{an}满足2an/an+2=an+1(n属于正整数),a1=1/1006.求证:数列{1/an}是等差数列,并求通项an已知数列{an}满足(2an)/(an+2)=a(n+1)(n属于正整数),a1=1/1006.求证:数列{1/an}是等差数列,并求通项an, 等差数列{an}满足a1=1,且a1、a2、a4成等比数列,求an