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.求a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.求an 通项
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.求a
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.求an 通项
答
1/an+1=√(4+1/an^2)
a2=√5/5
1/(an+1)^2=4+1/an^2
1/(an+1)^2-1/an^2=4
所以Tn=1/(an+1)^2是等差数列
T1=5
Tn=5+(n-1)*4=1/(an+1)^2=4n+1
所以an+1=√[1/(4n+1)]
an=√[1/(4n-3)] (n>=1)
答
1/an+1=√(4+1/an^2)a2=√5/51/(an+1)^2=4+1/an^21/(an+1)^2-1/an^2=4所以Tn=1/(an+1)^2是等差数列T1=5Tn=5+(n-1)*4=1/(an+1)^2=4n+1所以an+1=√[1/(4n+1)]an=√[1/(4n-3)] (n>=1)