数列An的前n项和 Sn=n^2-4n+4 求数列(1/An)的前n项和为Tn 若(T2n+1)-(Tn)小于等于m/15成立 正蒸数m最小值
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![数列An的前n项和 Sn=n^2-4n+4 求数列(1/An)的前n项和为Tn 若(T2n+1)-(Tn)小于等于m/15成立 正蒸数m最小值](/uploads/image/z/14601892-4-2.jpg?t=%E6%95%B0%E5%88%97An%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C+Sn%3Dn%5E2-4n%2B4+%E6%B1%82%E6%95%B0%E5%88%97%281%2FAn%29%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BATn+%E8%8B%A5%28T2n%2B1%29-%28Tn%29%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8Em%2F15%E6%88%90%E7%AB%8B+%E6%AD%A3%E8%92%B8%E6%95%B0m%E6%9C%80%E5%B0%8F%E5%80%BC)
数列An的前n项和 Sn=n^2-4n+4 求数列(1/An)的前n项和为Tn 若(T2n+1)-(Tn)小于等于m/15成立 正蒸数m最小值
数列An的前n项和 Sn=n^2-4n+4 求数列(1/An)的前n项和为Tn 若(T2n+1)-(Tn)小于等于m/15成立 正蒸数m最小值
数列An的前n项和 Sn=n^2-4n+4 求数列(1/An)的前n项和为Tn 若(T2n+1)-(Tn)小于等于m/15成立 正蒸数m最小值
n=1时,S1=a1=1-4+4=1
n≥2时,
Sn=n²-4n+4 S(n-1)=(n-1)²-4(n-1)+4
Sn-S(n-1)=an=n²-4n+4-(n-1)²+4(n-1)-4=2n-5
n=1时,a1=2-5=-3,与a1=1不符.
数列{an}的通项公式为
an=1 n=1
2n-5 n≥2
n=1时,T3-T1=1/a1+1/a2+1/a3-1/a1=1/a2+1/a3=1/(4-5)+1/(6-5)=-1+1=0
T3-T1≤m/15
m/15≥0
m≥0
n≥2时,
Tn=1/a1+1/a2+...+1/an
T(2n+1)=1/a1+1/a2+...+1/an+1/a(n+1)+1/a(n+2)+...+1/a(2n+1)
T(2n+1)-Tn=1/a(n+1)+1/a(n+2)+...+1/a(2n+1)
[T(2n+3)-T(n+1)]-[T(2n+1)-Tn]
=[1/a(n+2)+1/a(n+3)+...+1/a(2n+1)+1/a(2n+2)+1/a(2n+3)]-[1/a(n+1)+1/a(n+2)+...+1/a(2n+1)]
=1/a(2n+2)+1/a(2n+3)-1/a(n+1)
=1/a(2n+3)-1/(2n+2)