(本小题满分14分)设函数f (x)满足f (0) =1,且对任意,都有f (xy+1) = f (x) f (y)-f (y)-x+2.(I) 求f (x) 的解析式;(II) 若数列{an}满足:an+1=3f (an)-1(nÎ N*),且a1=1,求数列{an}的通项公式;
(Ⅲ)求数列{an}的前n项和Sn.
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(本小题满分14分)设函数f (x)满足f (0) =1,且对任意,都有f (xy+1) = f (x) f (y)-f (y)-x+2.(I) 求f (x) 的解析式;(II) 若数列{an}满足:an+1=3f (an)-1(nÎ N*),且a1=1,求数列{an}的通项公式;
(Ⅲ)求数列{an}的前n项和Sn.