∵An/Bn=(7n+45)/(n+3)
An/Bn=[(a1+an)n/2]/[(b1+bn)n/2]
=(a1+an)/(b1+bn)
(a1+an)/(b1+bn)=(7n+45)/(n+3)
(下面需将an/bn------> [a1+ax]/[b1+bx]形式)
∴an/bn=(2an)/(2bn)
=[a1+a(2n-1)]/[b1+b(2n-1)]
=[7(2n-1)+45]/[(2n-1)+3]
=(14n+38)/(2n+2)
=(7n+19)/(n+1)
=[7(n+7)+12]/(n+1)
=7+12/(n+1)
∵an/b2n为整数
∴n+1=2,3,4,6,12
∴n=1,2,3,5,11共5个
没看清楚,是an/b2n
∵An/Bn=(7n+45)/(n+3)
∴An=kn(7n+45),Bn=kn(n+3)
k为常数
an=An-A(n-1)
=7kn^2+45kn-7k(n-1)^2 -45k(n-1)
=14kn+38k
bn=Bn-B(n-1)
=kn^2+3kn-k(n-1)^2-3k(n-1)
=2kn+2k
an/b2n=(14kn+38k)/(4kn+2k)
=(7n+19)/(2n+1)
=[7(2n+1)+31]/[2(2n+1)]
=7/2+31/(4n+2)
∴31/(4n+2)的小数部分为0.5,
分母应为62,4n+2=62,n=15
一个
(4n+2=6,10,14,18,20,24,.,58均不合题意)