CN-LEAGUE 2008 Problem 3

For all $k=1,2,\ldots,2008$ , $a_k>0$ .Prove that iff $\sum_{k=1}^{2008}a_k>1$ ,there exists a function $f:N\rightarrow R$ satisfying (1) $0=f(0)<f(1)<f(2)<\ldots$ ; (2) $f(n)$ has a finite limit when $n$ approaches infinity; (3) $f(n)-f({n-1})=\sum_{k=1}^{2008}a_kf({n+k})-\sum_{k=0}^{2007}a_{k+1}f({n+k})$ ,for all $n=1,2,3,\ldots$ .