已知函数f(x)=3x/x+3(x不等于负3,x属于R),数列{a小n}满足a小n=f(a小n减1)(n大于等于2,n属于N)且a1不等...

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已知函数f(x)=3x/x+3(x不等于负3,x属于R),数列{a小n}满足a小n=f(a小n减1)(n大于等于2,n属于N)且a1不等...
已知函数f(x)=3x/x+3(x不等于负3,x属于R),数列{a小n}满足a小n=f(a小n减1)(n大于等于2,n属于N)且a1不等于0, (1)求证:数列{1/a小n}是等差数列(2)若a1=1/4,求a50的值 急

(1)设Bn=1/An
Bn - B(n-1)=1/f(A(n-1))-1/f(A(n-1))
=(f(A(n-1)) +3)/(3f(A(n-1)) ) - 1/f(A(n-1))
=1/3+1/f(A(n-1)) -1/f(A(n-1))
=1/3
(2)A1=0.25 B1=4
Bn是等差数列,Bn=n/3+11/3
所以An=3/(n+11)