在等差数列中,若Sm/Sn=m^2/n^2(m不等于n),则am/an=

原问题即 ：有两个数列,{An} {Bn},若 Sm :Sn = m^2 :n^2
求 Am :Bn (公差分别为d1,d2)
Sm = A1d + 0.5*m(m-1)d1 = 0.5d1m^2 + m(A1-0.5d1)
Sn = 0.5d2n^2 + n(B1-0.5d2)
∵ Sm :Sn = m^2 :n^2 ∴ A1-0.5d1=0 B1-0.5d2=0
Sm = 0.5d1m^2 Sn = 0.5d2n^2 ∴d1=d2=d A1=A2=0.5d
∵ Am = A1 + (m-1)d = d(m-0.5) Bn = d(n-0.5)
∴ Am :Bn = (m-0.5) :(n-0.5) = (2m-1) :(2n-1)