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Let

\{a_i\}

be a strictly increasing sequence of positive integers. Define the sequence

\{s_k\}

s_k = \sum_{i=1}^{k}\frac{1}{[a_i,a_{i+1}]},

where

[a_i,a_{i+1}]

is the least commun multiple of

a_i

and

a_{i+1}

. Show that the sequence

\{s_k\}

is convergent.

Problem 4