已知数列an满足a(n+1)=2an+3n^2+4n+5,a1=1,求数列an的通项公式
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/10/11 13:27:55
已知数列an满足a(n+1)=2an+3n^2+4n+5,a1=1,求数列an的通项公式
不要复制,要如何配凑的过程
不要复制,要如何配凑的过程
a(n+1)=2an+3n^2+4n+5
let
a(n+1) + k1(n+1)^2+k2(n+1)+k3=2(an+k1n^2+k2n+k3)
coef.of n^2
k1=3
coef.of n
k2-2k1=4
k2=10
coef.of constant
k3-k1-k2=5
k3=18
ie
a(n+1)=2an+3n^2+4n+5
a(n+1) + 3(n+1)^2+10(n+1)+18=2(an+3n^2+10n+18)
=>{an+3n^2+10n+18}是等比数列,q=2
an+3n^2+10n+18 = 2^(n-1) .(a1+3+10+18)
=2^(n+4)
an = -(3n^2+10n+18) +2^(n+4)
let
a(n+1) + k1(n+1)^2+k2(n+1)+k3=2(an+k1n^2+k2n+k3)
coef.of n^2
k1=3
coef.of n
k2-2k1=4
k2=10
coef.of constant
k3-k1-k2=5
k3=18
ie
a(n+1)=2an+3n^2+4n+5
a(n+1) + 3(n+1)^2+10(n+1)+18=2(an+3n^2+10n+18)
=>{an+3n^2+10n+18}是等比数列,q=2
an+3n^2+10n+18 = 2^(n-1) .(a1+3+10+18)
=2^(n+4)
an = -(3n^2+10n+18) +2^(n+4)
已知数列{an}满足a1=1,an=(an-1)/3an-1+1,(n>=2,n属于N*),求数列{an}的通项公式
已知数列{an}满足a1=1,an=4a(n-1)/[2a(n-1)+1] (n>=2)求数列{an}的通项公式
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
已知数列{An}满足An+1=2(n+1)*5的n次方*An,A1=3,用累乘法求数列{An}的通项公式
数列{an}满足递推式an=3a(n-1)+3^n-1(n>=2),又a1=5,求数列{an}的通项公式
已知数列{an}满足 a1=3,an+1=an+3n²+3n+2-1\n(n+1),求an的通项公式
已知数列{an}满足a1=b,an=nban-1/an-1+n-1(n大于等于2),求数列an的通项公式
已知数列an满足a1=1 2a(n+1)=an+3 N属于N* 求数列通项公式
已知数列{an}满足a1=1,a(n+1)=2an+1(n∈N)(1)求数列{an}的通项公式(2)若数列{bn}满足4
已知数列{an}满足a1=1,an+1=2an/(an+2)(n∈N+),则数列{an}的通项公式为
已知数列{An}满足A1=2,A(n+1)=2An/(2+An).(1)求此数列的前三项,(2)求{An}的通项公式
已知数列an满足a1=1,a(n+1)=an/(3an+1) 求数列通项公式