等差數(shù)列{an},{bn}的前n項(xiàng)和分別為Sn,Tn,若Sn/Tn＝2n/3n+1,則an/bn等于多少?
方法一:
Sn/Tn=2n/(3n+1),即
S(2n-1)/T(2n-1)=2(2n-1)/[3(2n-1)+1]=(2n-1)/(3n-1),即
[A1+A（2n-1）]/[B1+B(2n-1)]=(2n-1)/(3n-1),即
2An/2Bn=(2n-1)/(3n-1),
An/Bn=(2n-1)/(3n-1) 為什么上面要把2n-1帶進(jìn)去?有什么特別的意義嗎.
方法2:
:∵{an}與{bn}是等差數(shù)列
∴Sn=[n(a1+an)]/2
Tn=[n(b1+bn)]/2
∴Sn/Tn=(a1+an)/(b1+bn)
∵等差數(shù)列{an}與{bn}的前n項(xiàng)和的比為2n:(3n+1)
∴(a1+an)/(b1+bn)=2n:(3n+1)
假設(shè)(n+1)/2 =k {(n+1)/2為項(xiàng)數(shù)}
則n=2k-1
則ak/bk = 2(2k-1)/[3(2k-1)+1]
=(2k-1)/(3k-1) (n+1)/2為項(xiàng)數(shù)``這句話什么意思?為什么我怎么看都不像是項(xiàng)數(shù)..