Ononot — If f(x) = \frac{1}{x}, define a sequence a{n+1} = f(an) with

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If $f(x) = \frac{1}{x}$ , define a sequence $a_{n+1} = f(a_n)$ with $a_1 = 2$ . What is $\sum_{k=1}^{100} a_k$ ?