高一数列难题已知f(x)=-根号下4+1/x^2,点Pn(an,-1/a(n+1))在y=fx上 a1=1 an大于0 (1)求an的通向公式(2)数列bn的前n项和Tn满足Tn+1/an^2=Tn/an^2+1+16n^2-8n-3当b1取何值时使得bn是等差数列
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![高一数列难题已知f(x)=-根号下4+1/x^2,点Pn(an,-1/a(n+1))在y=fx上 a1=1 an大于0 (1)求an的通向公式(2)数列bn的前n项和Tn满足Tn+1/an^2=Tn/an^2+1+16n^2-8n-3当b1取何值时使得bn是等差数列](/uploads/image/z/14150042-26-2.jpg?t=%E9%AB%98%E4%B8%80%E6%95%B0%E5%88%97%E9%9A%BE%E9%A2%98%E5%B7%B2%E7%9F%A5f%EF%BC%88x%EF%BC%89%3D-%E6%A0%B9%E5%8F%B7%E4%B8%8B4%2B1%2Fx%5E2%2C%E7%82%B9Pn%EF%BC%88an%2C-1%2Fa%28n%2B1%29%29%E5%9C%A8y%3Dfx%E4%B8%8A+a1%3D1+an%E5%A4%A7%E4%BA%8E0+++++%EF%BC%881%EF%BC%89%E6%B1%82an%E7%9A%84%E9%80%9A%E5%90%91%E5%85%AC%E5%BC%8F%EF%BC%882%EF%BC%89%E6%95%B0%E5%88%97bn%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CTn%E6%BB%A1%E8%B6%B3Tn%2B1%2Fan%5E2%3DTn%2Fan%5E2%2B1%2B16n%5E2-8n-3%E5%BD%93b1%E5%8F%96%E4%BD%95%E5%80%BC%E6%97%B6%E4%BD%BF%E5%BE%97bn%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97)
高一数列难题已知f(x)=-根号下4+1/x^2,点Pn(an,-1/a(n+1))在y=fx上 a1=1 an大于0 (1)求an的通向公式(2)数列bn的前n项和Tn满足Tn+1/an^2=Tn/an^2+1+16n^2-8n-3当b1取何值时使得bn是等差数列
高一数列难题
已知f(x)=-根号下4+1/x^2,点Pn(an,-1/a(n+1))在y=fx上 a1=1 an大于0 (1)求an的通向公式(2)数列bn的前n项和Tn满足Tn+1/an^2=Tn/an^2+1+16n^2-8n-3当b1取何值时使得bn是等差数列
高一数列难题已知f(x)=-根号下4+1/x^2,点Pn(an,-1/a(n+1))在y=fx上 a1=1 an大于0 (1)求an的通向公式(2)数列bn的前n项和Tn满足Tn+1/an^2=Tn/an^2+1+16n^2-8n-3当b1取何值时使得bn是等差数列
(1) 令1/an=bn,则,b1=1/a1=1;b(n+1)=1/a(n+1); [b(n+1)]^2=4+bn^2
错位相减:b2^2+b3^2+...+bn^2+b(n+1)^2=4+b1^2+4+b2^2+4+b3^2+...+4+bn^2
b(n+1)^2=4n+b1^2=4n+1
a(n+1)=1/√(4n+1);an=1/√(4n-3)
(2)
Tn(1-1/an^2)=(1-1/an^2)+(4n+1)(4n-3)
当Tn=-n(n+2)时【非唯一解,2可以是其他任意正整数,合理即可,因为是数列】,bn是等差数列
此时,T1=b1=-3
T2=b1+b2=-3+b2=-8,b2=-5
T3=T2+b3=-8+b3=-15,b3=-7
T4=T3+b4=-15+b4=-24,b4=-9
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A=-1,由Tn=1+(4n+1)(4n-3)/(1-1/an^2)=-n(n+2)可推出an=?
此略: