# Reciprocals of each other.

Algebra Level 2

Consider an arithmetic progression with terms $$a_1, a_2, \ldots$$ and the sum of the first $$k$$ terms is $$S_k$$. If

$a_{13} = \frac{1}{11} , a_{11} = \frac{1}{13},$

then find $$S_{143}$$.

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