已知数列an满足a(n+1)=an-a(n-1) (n≥2) ,a1=1 ,a2=3 ,记Sb=a1+a2+...+an ,则 a100=?S100=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/17 05:33:35
已知数列an满足a(n+1)=an-a(n-1) (n≥2) ,a1=1 ,a2=3 ,记Sb=a1+a2+...+an ,则 a100=?S100=?
已知数列an满足a(n+1)=an-a(n-1) (n≥2) ,a1=1 ,a2=3 ,记Sb=a1+a2+...+an ,则 a100=?S100=?
已知数列an满足a(n+1)=an-a(n-1) (n≥2) ,a1=1 ,a2=3 ,记Sb=a1+a2+...+an ,则 a100=?S100=?
(1)
n≥2时,
a(n+1)=an-a(n-1)
a(n+2)=a(n+1)-an
a(n+2)+a(n+1)=a(n+1)-a(n-1)
a(n+2)=-a(n-1)
a(n+3)=-an
a(n+6)=-a(n+3)=an
数列{an}是以6为周期的周期数列
a100=a(6×16+4)=a4=-a(4-3)=-a1=-1
(2)
a3=a2-a1=3-1=2
a(n+1)=an-a(n-1)
an=a(n-1)-a(n-2)
a(n-1)=a(n-2)-a(n-3)
…………
a3=a2-a1
累加
a3+a4+...+an=a(n-1)-a1
Sn=a1+a2+a3+...+an=a1+a2+a(n-1)-a1=a2+a(n-1)
S100=a2+a(100-1)=a2+a99
a99=a(6×16+3)=a3=2
S100=a2+a99=3+2=5
已知数列{an}满足a(n+1)=an+n,a1=1,则an=
已知数列{an}满足a(n+1)=an+lg2,a1=1,求an
周期性数列问题i已知数列{an}满足a(n+1)=2an (0
已知数列an满足a1=1,a(n+1)=an/(3an+1) 求数列通项公式
已知数列{an}满足a1=2,a(n+1)-an=a(n+1)*an,则a31=?
已知数列an满足a1=1,a(n+1)=an/(3an+2),则an=?
已知数列an满足条件a1=-2 a(n+1)=2an/(1-an) 则an=
已知数列an满足1/a-an=2根号n,且an>0.求an的通项公式是数列{an}满足1/an-an=2根号n,且an>0,求an的通项公式。
已知数列an满足:a1=1,an-a(n-1)=n n大于等于2 求an
已知数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值
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a1=100,a(n+1)-an=2n,则(an)/n的最小值为
已知数列an满足a1=2,an=a(n-1)+2n,(n≥2),求an
已知数列{an}满足a1=1,3a(n+1)+an-7
已知数列{An}满足A(n+1)=【2An (0
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=5,a(n+1)=an+6n+6,则an=
已知数列an满足a(n+1)=an+3n+2,且a1=2,求an