已知数列(An)满足:A1=1,2^(n-1)*An=A下标(n-1) (n为正整数),n≥2 (1)求数列(An)的通项公式已知数列(An)满足:A1=1,2^(n-1)*An=A下标(n-1)(n为正整数),n≥2(1)求数列(An)的通项公式(2)这个数列从第几项开始以后各
来源:学生作业学帮网 编辑:学帮网 时间:2024/05/21 05:56:31
已知数列(An)满足:A1=1,2^(n-1)*An=A下标(n-1) (n为正整数),n≥2 (1)求数列(An)的通项公式
已知数列(An)满足:A1=1,2^(n-1)*An=A下标(n-1)
(n为正整数),n≥2
(1)求数列(An)的通项公式
(2)这个数列从第几项开始以后各项均小于1/1000
(1)2^(n-1)*An=A(n-1),则A(n-1)/An=2^(n-1),
于是(A1/A2)*(A2/A3)*...*[A(n-1)/An]=A1/An=2*(2^2)*...*[2^(n-1)]=2^[1+2+...+(n-1)]
=2^{[1+(n-1)]*n/2}=2^[(n^2)/2],
因为A1=1,代入上式,An=2^[-(n^2)/2]
(2)有An=1/{2^[(n^2)/2]},则使An1000,n=4时,M=256,n=5时,M>2^10
于是,自A5项开始,以后各项均小于1/1000
(1)A_n / A_{n-1} = 2 ^ (-(n-1)), A_n = [A_n / A_{n-1}] * [A_{n-1} / A_{n-2}] * ... * [A_2 / A_1] * A_1 = 2 ^ {n(n-1)/2}
(2)由(1)得:n = 5
已知数列{an}满足an+1=2an+3.5^n,a1=6.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}满足a1=1,an+1·an=2^n 则s2012
已知数列{an}满足a1=1/2,sn=n^2an,求通项an
已知数列{an},满足a1=1/2,Sn=n²×an,求an
已知数列an满足a1=1/2 sn=n平方×an 求an
已知数列An满足 A1=1/2 Sn=N²An 求An
已知数列an满足a1=1 Sn=2an+n 求an
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
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a1=1 ,Sn=(n+1)*an/2,求通项 的表达式.
已知数列an满足an+1/an=n+2/n且a1=1,则an=
已知数列{an}满足a1=1/2,an+1=an+1/n的平方+n求an
已知数列an满足a1=1/2,an+1=an+1/n²+n,求an
已知数列{an}满足a1=33,an+1-an=2n 则求an/n的最小值
已知数列{an}满足a1=33,an+1-an=2n 则求an/n?
已知数列an满足a1=33 an+1 -an=2n 则an/n的最小值是?
已知数列{an}满足a1=33,an+1-an=2n,则an/n的最小值为