已知数列{an}满足a(n+1)=2an+n^2,a1=2
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/28 21:33:32
已知数列{an}满足a(n+1)=2an+n^2,a1=2
bn=an+n^2+2n+3,(n∈N*)
(1)求证{bn}为等比数列(2)求{an}通项公式
bn=an+n^2+2n+3,(n∈N*)
(1)求证{bn}为等比数列(2)求{an}通项公式
(1)因为bn=an+n^2+2n+3,a(n+1)=2an+n^2,所以b(n+1)=a(n+1)+(n+1)^2+2(n+1)+3=2an+2n^2+4n+6
b(n+1)/bn=2
所以{bn}为等比数列.
(2)因为a1=2,所以b1=a1+1^2+2+3=8
所以bn=8*2^(n-1)=2^(n+2)
所以an=bn-2n-3=2^(n+2)-2n-3
b(n+1)/bn=2
所以{bn}为等比数列.
(2)因为a1=2,所以b1=a1+1^2+2+3=8
所以bn=8*2^(n-1)=2^(n+2)
所以an=bn-2n-3=2^(n+2)-2n-3
已知数列{an}满足a1=100,an+1-an=2n,则a
已知数列{an}满足,a1=2,a(n+1)=3根号an,求通项an
已知数列{an}满足a1=33,a(n+1)-an=2n,求an/n的最小值
已知数列{an}满足an+1=2an+3.5^n,a1=6.求an
已知数列{an}满足a1=1,2a(n+1)an+3a(n+1)+an+2=0.
已知数列{an}满足a1=4/3,2-a(n+1)=12/an+6
已知数列{an}满足a(n+1)=an+3n+2,且a1=2,求an=?
已知数列an满足a(n+1)=an+3n+2,且a1=2,求an
已知数列{An}满足A1=1,A=3(n-1)+A(n>/2)
已知数列{an}中,a1=1,满足an+1=an+2n,n属于N*,则an等于
已知数列{an}满足a1=1;an=a1+2a2+3a3+...+(n-1)a(n-1);
已知数列an满足条件a1=-2 a(n+1)=2an/(1-an) 则an=