数列an满足an+1 - an + an-1=0 (n≥2),且a1=1,a2=-1,则a2011= a.1 b.-1 c.2 d.-2

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/07 20:53:44
数列an满足an+1 - an + an-1=0 (n≥2),且a1=1,a2=-1,则a2011= a.1 b.-1 c.2 d.-2

数列an满足an+1 - an + an-1=0 (n≥2),且a1=1,a2=-1,则a2011= a.1 b.-1 c.2 d.-2
数列an满足an+1 - an + an-1=0 (n≥2),且a1=1,a2=-1,则a2011= a.1 b.-1 c.2 d.-2

数列an满足an+1 - an + an-1=0 (n≥2),且a1=1,a2=-1,则a2011= a.1 b.-1 c.2 d.-2
an+1 - an + an-1=0 (n≥2)且a1=1,a2=-1,
an-an-1+an-2=0
相加,得
an+1+an-2=0
an+1=-an-2=an-5
所以
以6为周期
2011÷6=335...1
所以
a2011=a1=1
选a

A