数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 13:37:06

数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2
数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2

数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2
（Ⅰ）由an+2=2an+1-an+2得,
an+2-an+1=an+1-an+2,
由bn=an+1-an得,bn+1=bn+2,
即bn+1-bn=2,
又b1=a2-a1=1,
所以{bn}是首项为1,公差为2的等差数列．
（Ⅱ）由（Ⅰ）得,bn=1+2（n-1）=2n-1,
由bn=an+1-an得,an+1-an=2n-1,
则a2-a1=1,a3-a2=3,a4-a3=5,…,an-an-1=2（n-1）-1,
所以,an-a1=1+3+5+…+2（n-1）-1
=
(n−1)(1+2n−3)
2
=（n-1）2,
又a1=1,
所以{an}的通项公式an=（n-1）2+1=n2-2n+2．

数列{An}满足a1=1/2,a1+a2+..+an=n方an,求an 若数列an满足a1＝1/2.a1+a2+a3+……+an＝n^2an则数列an的前60项和为数列{an}满足a1＝1／2,a1＋a2＋……＋an＝n的平方×an,则数列{an}的通项公式? 已知数列{an}满足a1＝1,an=a1＋1/2a2＋1/3a3+…＋1/(n－1)an 数列{an}满足a1＝1,a2＝2,an＋2＝2an＋1－an＋2 已知数列an满足an=1+2+...+n,且1/a1+1/a2+...+1/an 数列an满足a1=1/2,a1+a2+a3……an=n^2an,则an 已知数列{an}满足a1=1,a2=3,an+2=3an+1-2an求an 已知数列（an）满足a1=1,an=a1+2a2+3a3+.+（n-1)an-1,则n≥2时,数列｛an｝的通项an＝设正数列a0,a1,a2,…,an,…满足 (n≥2)且a0=a1=1.求{an}的通项公式.设正数列a0,a1,a2,…,an,…满足 (n≥2)且a0＝a1＝1．1.证明√（an/an-1)成等差数列2.求{an}的通项公式．已知数列an'满足a1=1/2,a1+a2+a3+...+an=n^2an,求通项公式设数列AN满足A1等于1,3(A1+a2+~+AN)=(n+2)an,求通向公式已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman 已知数列an满足a1=0 a2=1 an=(An-1+An-2)/2 求liman 数列An,满足An=An-1 + An-2,其中,A1=1,A2=1,求通项公式. 若数列{an}满足a1=1,a2=5且an+2=an+1-an,求a2000 数列{an}满足a1=3,a2=6,an+2=an+1-an,求a2013 数列{an}满足a1=3,a2=6,an+2=an+1-an,求a2008