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
- \(1\), (b) \(\dfrac{6}{5}\), (c) \(\dfrac{8}{5}\), (d) \(3\), (e) \(\dfrac{27}{5}\).
Can we write the sequence \(x_0, x_1, x_2,...\) out? What kind of a sequence is this (almost)?
So what kind of a sequence is \(\dfrac{1}{x_n}\) (almost)?
How do we sum this kind of sequence?
