已知数列{an}满足2a1+2^2a2+2^3a3+...+2^nan=4^n-1,则{an}的通项公式2a1+2^2a2+2^3a3就是2a1+4a2+8a3...

来源：学生作业帮助网编辑：作业帮时间：2024/05/09 10:27:28

$已知数列{an}满足2a1+2^2a2+2^3a3+...+2^nan=4^n-1,则{an}的通项公式2a1+2^2a2+2^3a3就是2a1+4a2+8a3...$

已知数列{an}满足2a1+2^2a2+2^3a3+...+2^nan=4^n-1,则{an}的通项公式2a1+2^2a2+2^3a3就是2a1+4a2+8a3...
已知数列{an}满足2a1+2^2a2+2^3a3+...+2^nan=4^n-1,则{an}的通项公式
2a1+2^2a2+2^3a3就是2a1+4a2+8a3...

已知数列{an}满足2a1+2^2a2+2^3a3+...+2^nan=4^n-1,则{an}的通项公式2a1+2^2a2+2^3a3就是2a1+4a2+8a3...
2A1=4^(1-1)
A1=1/2
2A1+2^2A2+2^3A3+……+2^(n-1)A(n-1)+2^nAn=4^(n-1)
2A1+2^2A2+2^3A3+……+2^(n-1)A(n-1)=4^(n-2)
两式相减
2^nAn=4^(n-1)-4^(n-2)=3×4^(n-2)
An=3×4^(n-2)/2^n=3×2^(2n-4)/2^n=3×2^(n-4)
A1=1/2

首先求a1， 2a1=4-1=3 a1=3/2 设右边的式子为Sn
2^nan=Sn-Sn-1=4^n-1-[4^(n-1)-1]=2^2n-2^(2n-2)=3x2^(2n-2)
所以2^nan=3x2^(2n-2)
an=3x2^(n-2)
经验证，a1符合上式，所以 an=3x2^(n-2)

已知数列an满足an=1+2+...+n,且1/a1+1/a2+...+1/an 已知数列{an}满足：a1+a2+a3+.+an=n^2,求数列{an}的通项an. 已知数列an'满足a1=1/2,a1+a2+a3+...+an=n^2an,求通项公式已知数列{an}满足a1=1,a2=3,an+2=3an+1-2an求an 已知数列满足a1=1/2,an+1=2an/(an+1),求a1,a2已知数列满足a1=1/2,a(n+1)=2an/(an+1),求a1,a2;证明0 数列{An}满足a1=1/2,a1+a2+..+an=n方an,求an 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 几个数列问题.已知数列{an} a1=1,an+1=an/(1+n^2*an) 求an 已知数列{an} 满足a1=1 a1*a2*a3.*an=n^2 求an 已知数列an满足an=1+2+...n,且（1/a1）+(1/a2）+...(1/an) 已知数列{an}中满足a1=1,a(n+1)=2an+1 (n∈N*),证明a1/a2+a2/a3+…+an/a(n+1) 已知数列{an}满足条件:a1=5,an=a1+a2+...a(n-1) n大于等于2,求数列{an}的通项公式已知递增数列{an}满足a1=1,(2an+1)=an+(an+2),且a1,a2,a4成等比数列.求an 已知数列{an}满足:a1=1,且an-an-1=2n,求(1)a2,a3,a4.(2)求数列{an}的通项an 关于数列极限的已知数列an满足a1=0 a2=1 an=(an-1+an-2)/2 求lim(n->无穷）an 已知数列(an)满足a1=1,an+1=2an/an+2(n∈N*) 求a2,a3,a4,a5 猜想数列(an)的通项公 (1)数列{an}中,a1=1,a2=-3,a(n+1)=an+a(n+2),则a2005=____(2)已知数列｛an｝满足a1=1,a1×a2×a3…an=n^2,求an. 已知数列an中 a1=1a2=2