Review question

# Given the sequence $(x_n)$, what is $\sum_{k=0}^\infty 1/x_k$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8248

## Suggestion

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) $\dfrac{27}{5}$.

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?