Given the sequence $(x_n)$, what is $\sum_{k=0}^\infty 1/x_k$?

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The sequence \((x_n)\), where \(n \geq 0\), is defined by \(x_0 =1\) and

\[x_n = \sum_{k=0}^{n-1}x_k \quad \text{for} \quad n \geq 1.\]

The sum

\[\sum_{k=0}^\infty \dfrac{1}{x_k}\]

equals

1. \(1\), (b) \(\dfrac{6}{5}\), (c) \(\dfrac{8}{5}\), (d) \(3\), (e) \(\dfrac{27}{5}\).