已知f(x)=根号下4+1/x2,数列{an}的前n项和为Sn,点Pn(an,-1/an+1)(n属于N*)在曲线y=f(x)上,且a1=1,an>0.已知f(x)=根号下4+1/x2,数列{an}的前n项和为Sn,点Pn(an,1/an+1)(n属于N*)在曲线y=f(x)上,且a1=1,an>0.(1)求数列{an}的通项公式(2)数列{bn}的首项b1=1,前n项和为Tn,且Tn+1/a2n=Tn/a2n+1+16n2-8n-3,设定b1的值使数列{bn}是等差数列(3)求证Sn大于1/2根号下4n+1-1
问题描述:
已知f(x)=根号下4+1/x2,数列{an}的前n项和为Sn,点Pn(an,-1/an+1)(n属于N*)在曲线y=f(x)上,且a1=1,an>0.
已知f(x)=根号下4+1/x2,数列{an}的前n项和为Sn,点Pn(an,1/an+1)(n属于N*)在曲线y=f(x)上,且a1=1,an>0.
(1)求数列{an}的通项公式
(2)数列{bn}的首项b1=1,前n项和为Tn,且Tn+1/a2n=Tn/a2n+1+16n2-8n-3,设定b1的值使数列{bn}是等差数列
(3)求证Sn大于1/2根号下4n+1-1
答
(1)√(4+1/an^2)=1/a(n+1)所以4+1/an^2=1/a(n+1)^2所以{1/an^2}为首项1/a1^2=1,公比为4的等差数列1/an^2=4n-3an=√[1/(4n-3)](2)?题目有问题,b1=1啊,怎么还要设定?(3)1.当n=1时,Sn=a1=11/2√(4n+1)-1=(√5-2)/2左边>...