<prompt> Tafutaprod_k 0infty kushoto 1 frac1142k kulia.  <response>: Kwa ujumla zaidi, fikiriaprod_k 0infty 1 x2k 1 x1 x21 x4 dotsm.ambapo x 1. Bidhaa iliyo kwenye tatizo ni pale x frac114.Tunaweza kuandika1 x2k frac1 x2k1 - x2k1 - x2k frac1 - x2k 11 - x2k.Kwa hiyo,1 x1 x21 x4 dotsm frac1 - x21 - x cdoti frac1 - x4 1 - x2 cdot frac1 - x81 - x4 dotsm frac11 - x.Kwa x frac1101 14, hii ni frac11 - frac114 frac1413. 