已知数列{an}和{bn},{an}的前n项和为Sn,a2=0,且对任意n∈N*都有2Sn=n(an-1),点列Pn(an,bn)都在直线上直线为:y=2x+2(1)求数列{an}的通项公式(2)求证1/(│向量P1P2│)^2+1/(│向量P1P3│)^2+…+1/(│向量
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![已知数列{an}和{bn},{an}的前n项和为Sn,a2=0,且对任意n∈N*都有2Sn=n(an-1),点列Pn(an,bn)都在直线上直线为:y=2x+2(1)求数列{an}的通项公式(2)求证1/(│向量P1P2│)^2+1/(│向量P1P3│)^2+…+1/(│向量](/uploads/image/z/13636857-57-7.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E5%92%8C%7Bbn%7D%2C%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2Ca2%3D0%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8Fn%E2%88%88N%2A%E9%83%BD%E6%9C%892Sn%3Dn%28an-1%29%2C%E7%82%B9%E5%88%97Pn%EF%BC%88an%2Cbn%29%E9%83%BD%E5%9C%A8%E7%9B%B4%E7%BA%BF%E4%B8%8A%E7%9B%B4%E7%BA%BF%E4%B8%BA%EF%BC%9Ay%3D2x%2B2%281%29%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%282%29%E6%B1%82%E8%AF%811%2F%EF%BC%88%E2%94%82%E5%90%91%E9%87%8FP1P2%E2%94%82%EF%BC%89%5E2%2B1%2F%EF%BC%88%E2%94%82%E5%90%91%E9%87%8FP1P3%E2%94%82%EF%BC%89%5E2%2B%E2%80%A6%2B1%2F%EF%BC%88%E2%94%82%E5%90%91%E9%87%8F)
已知数列{an}和{bn},{an}的前n项和为Sn,a2=0,且对任意n∈N*都有2Sn=n(an-1),点列Pn(an,bn)都在直线上直线为:y=2x+2(1)求数列{an}的通项公式(2)求证1/(│向量P1P2│)^2+1/(│向量P1P3│)^2+…+1/(│向量
已知数列{an}和{bn},{an}的前n项和为Sn,a2=0,且对任意n∈N*都有2Sn=n(an-1),点列Pn(an,bn)都在直线上
直线为:y=2x+2
(1)求数列{an}的通项公式
(2)求证1/(│向量P1P2│)^2+1/(│向量P1P3│)^2+…+1/(│向量P1Pn│)^2<2/5(n≥2,n∈N*)
已知数列{an}和{bn},{an}的前n项和为Sn,a2=0,且对任意n∈N*都有2Sn=n(an-1),点列Pn(an,bn)都在直线上直线为:y=2x+2(1)求数列{an}的通项公式(2)求证1/(│向量P1P2│)^2+1/(│向量P1P3│)^2+…+1/(│向量
2*a1=2*a1=a1-1
a1=-1
n>=2时
2*Sn=n*an-n
2*S(n-1)=n*a(n-1)-a(n-1)-n+1
(n-2)an=(n-1)a(n-1)+1
n>=3时
an/(n-1)=a(n-1)/(n-2)+1/((n-2)(n-1))
a2=0
an/(n-1)=a2+1/(1*2)+1/(2*3)+……+1/((n-2)(n-1))=(n-2)/(n-1)
an=n-2
代入n=1,2时亦符合
故an=n-2
bn=2*an+2=2n-2
Pn(n-2,2n-2)
P1(-1,0)
(P1Pn)^2=(n-2+1)^2+(2n-2)^2=5*(n-1)^2
原式=(1/5)*(1/1^2+1/2^2+1/3^2+……+1/(n-1)^2)