数列{an}满足a1=a2=1,an+an+1+an+2=cos2nπ/3若数列{an}的前n项和为sn则s2012的值
问题描述:
数列{an}满足a1=a2=1,an+an+1+an+2=cos2nπ/3若数列{an}的前n项和为sn则s2012的值
答
∵2010=670×3∴a2010+a2011+a2012=cos(2010×2π/3)=cos(670×2π)=cos(2π)=1同理:a2007+a2008+a2009=cos(2007×2π/3)=cos(2π)=1.a3+a4+a5=cos(2π)=1 ∴s2012=(a2012+a2011+a2010)+(a2009+a2008+a2007)+.+(a5+...