HMMT 2008 U11

Let $f(r)=\sum_{j=2}^{2008} \frac{1}{j^{r}}=\frac{1}{2^{r}}+\frac{1}{3^{r}}+\cdots+\frac{1}{2008^{r}}$ . Find $\sum_{k=2}^{\infty} f(k)$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{2007}{2008}

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