Conjecture:

There is no $b,{a_n}_{n=1}^{infty}$ such

that $b,a_n in mathbb{N}^+, a_{n+1}ge a_n,lim_{nrightarrow infty}frac{a_n}{a_{n+1}}=0$ and

$$frac{1}{b}= sum_{n=1}^{infty}frac{1}{a_{n}}$$

This is just my guess, and it would be nice if someone could give a counter example.