Reciprocals of each other.

Algebra Level 2

Consider an arithmetic progression with terms a1,a2, a_1, a_2, \ldots and the sum of the first kk terms is SkS_k . If

a13=111,a11=113, a_{13} = \frac{1}{11} , a_{11} = \frac{1}{13},

then find S143 S_{143} .

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