Sequence of positive integers such that their reciprocals are in arithmetic progression Let $m_1 < m_2 < \ldots < m_k$ be $k$ distinct positive integers such that their reciprocals $\dfrac{1}{m_i}$ are in arithmetic progression. 


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*Show that $k < m_1 + 2$.

*Give an example of such a sequence of length $k$ for any positive integer $k$.


Any kind of help would be appreciated. 

Let the numbers $1/m_i$ be $1/N,2/N,3/N,...,k/N$ for suitable $N$.
