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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