Ononot — If f(x) = \frac{1}{x}, find \sum{k=1}^{100} ak where a1 = 2

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If $f(x) = \frac{1}{x}$ , find $\sum_{k=1}^{100} a_k$ where $a_1 = 2$ and $a_{n+1} = f(a_n)$ .