设等差数列{an},{bn} 的前n项和Sn,Tn满足Sn/Tn=An+1/2n+7,且a3/(b4+b6)+a7/(b
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设等差数列{an},{bn} 的前n项和Sn,Tn满足Sn/Tn=An+1/2n+7,且a3/(b4+b6)+a7/(b2+b8)=2/5,S2=6
函数g(x)=1/2(x-1),且Cn=g(Cn-1)(n∈N,n>1),c1=1.
(1)求An
(2)求数列{an}{cn}的通项公式
3 若d=an(n为奇数);d=cn(n为偶数)求d1+d2+……dn
函数g(x)=1/2(x-1),且Cn=g(Cn-1)(n∈N,n>1),c1=1.
(1)求An
(2)求数列{an}{cn}的通项公式
3 若d=an(n为奇数);d=cn(n为偶数)求d1+d2+……dn
![设等差数列{an},{bn} 的前n项和Sn,Tn满足Sn/Tn=An+1/2n+7,且a3/(b4+b6)+a7/(b](/uploads/image/z/15905664-0-4.jpg?t=%E8%AE%BE%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%2C%7Bbn%7D+%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%2CTn%E6%BB%A1%E8%B6%B3Sn%2FTn%3DAn%2B1%2F2n%2B7%2C%E4%B8%94a3%2F%28b4%2Bb6%29%2Ba7%2F%28b)
(1)
a3/(b4+b6) +a7/(b2+b8)=a3/(2*b5)+a7/(2*b5)=a5/b5=2/5
a5/b5=S9/T9=(9A+1)/(2*9+7)=(9A+1)/25=2/5
A=1
(2)
S2=k*2*(2A+1)=k*2*3=6
k=1
Sn=n(n+1)
S(n-1)=n(n-1)
an=2n
y=g(x)=1/2(x-1)
g(x)=(1/2)*(x-1)
cn=1/2 *[c(n-1)-1]
设
cn-m=1/2*[c(n-1)-m]
1/2m=-1/2 m=-1
cn+1=1/2[c(n-1)+1]
cn+1/[c(n-1)+1]=1/2
(cn + 1)/(c1+1)=(1/2)^(n-1)
c1=1
cn=1/2^(n-2)-1
(3)
当n是偶数的时候
不妨设n=2k
则sn=s2k=a1+a3+……+a(2k-1)+c2+c4+……+c2k
=2(1+3+……+2k-1)+1/2^0-1+1/2^2-1+1/2^2k-1
=2*2k *k/2+(1-1/2^(2k+2))*4/3-k
=2k^2+4/3-1/3*(1/2)^2k-k
把k替换成n/2即可
当n是奇数的时候
n=2k+1
sn=s2k=a1+a3+……+a(2k-1)+a(2k+1)+c2+c4+……+c2k
=2k^2+4/3-1/3*(1/2)^2k-k+2*(2k+1)
=2(k+1)^2+4/3-1/3*(1/2)^2k-k
把k替换成(n-1)/2即可
a3/(b4+b6) +a7/(b2+b8)=a3/(2*b5)+a7/(2*b5)=a5/b5=2/5
a5/b5=S9/T9=(9A+1)/(2*9+7)=(9A+1)/25=2/5
A=1
(2)
S2=k*2*(2A+1)=k*2*3=6
k=1
Sn=n(n+1)
S(n-1)=n(n-1)
an=2n
y=g(x)=1/2(x-1)
g(x)=(1/2)*(x-1)
cn=1/2 *[c(n-1)-1]
设
cn-m=1/2*[c(n-1)-m]
1/2m=-1/2 m=-1
cn+1=1/2[c(n-1)+1]
cn+1/[c(n-1)+1]=1/2
(cn + 1)/(c1+1)=(1/2)^(n-1)
c1=1
cn=1/2^(n-2)-1
(3)
当n是偶数的时候
不妨设n=2k
则sn=s2k=a1+a3+……+a(2k-1)+c2+c4+……+c2k
=2(1+3+……+2k-1)+1/2^0-1+1/2^2-1+1/2^2k-1
=2*2k *k/2+(1-1/2^(2k+2))*4/3-k
=2k^2+4/3-1/3*(1/2)^2k-k
把k替换成n/2即可
当n是奇数的时候
n=2k+1
sn=s2k=a1+a3+……+a(2k-1)+a(2k+1)+c2+c4+……+c2k
=2k^2+4/3-1/3*(1/2)^2k-k+2*(2k+1)
=2(k+1)^2+4/3-1/3*(1/2)^2k-k
把k替换成(n-1)/2即可
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