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已知函数f（x）=ax 3 +bx 2 +cx+d（a，b，c，d∈R，且a≠0），且函数f（x）图象关于原点中心对称，其图象在x=3处的切线方程为8x-y-18=0， 且 g(x)= f / (x)+ f / ( 3 ) ． （1）求函数f（x）的解析式； （2）若 f(x)＞ 3 2 x 2 -3x+ a 2 +a 在[0，2]上恒成立，求实数a的取值范围； （3）若数列{a n }满足a n+1 =g（a n ），a 1 =2，（n∈N * ）， 试证明： 1 a 1 + 1 a 2 +…+ 1 a n ＜ 7 8
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