等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n...等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n+c (1)求c 值(2)
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![等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n...等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n+c (1)求c 值(2)](/uploads/image/z/2707533-45-3.jpg?t=%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97an+%E4%B8%AD%2Can%2B1%E3%80%89an%2Ca2%2Ca4%E4%B8%BA%E6%96%B9%E7%A8%8Bx2-10x+%2B21%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%2C%E5%89%8Dn+%E9%A1%B9%E5%92%8CSn+%2C%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97bn%E7%9A%84%E5%89%8Dn+%E9%A1%B9%E5%92%8CTn+%3D3n...%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97an+%E4%B8%AD%2Can%2B1%E3%80%89an%2Ca2%2Ca4%E4%B8%BA%E6%96%B9%E7%A8%8Bx2-10x+%2B21%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%2C%E5%89%8Dn+%E9%A1%B9%E5%92%8CSn+%2C%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97bn%E7%9A%84%E5%89%8Dn+%E9%A1%B9%E5%92%8CTn+%3D3n%2Bc+%281%29%E6%B1%82c+%E5%80%BC%282%29)
等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n...等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n+c (1)求c 值(2)
等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n...
等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n+c (1)求c 值(2)证明:对n 为正整数,Sn -Tn 〈1,(3)证明:对任意n 为正整数,n(n+1)〉4Log3(n!)
Tn=3的n 方+c
等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n...等差数列an 中,an+1〉an,a2,a4为方程x2-10x +21=0的两根,前n 项和Sn ,等比数列bn的前n 项和Tn =3n+c (1)求c 值(2)
0=x^2-10x+21=(x-3)(x-7)
a(4)>a(3)>a(2)
a(4)=7,3=a(2).d=2,a=1
s(n)=n+n(n-1)=n^2
b(n+1)=T(n+1)-T(n)=2*3^n
b(1)=T(1)=3+c
c=-1
T(n)=3^n-1
归纳法可证n^2<3^n,2n+1<=3^n
(3)也用归纳法
Sn=n^2
1﹑c=-1
2﹑3^n=(2+1)^n>2^2*n(n-1)/2+2n+1=2n^2+1
3^n>n^2﹐Sn –Tn<1
3﹑证明改为3^[n(n+1)]>(n!)^4
开方得3^[n(n+1)/2]>(n!)^2
3^(1+2+…+n)=3^1*3^2*…*3^n>1^2*2^2*…*n^2
由3^n>n^2﹐即可证