<prompt> Mfuatano wa x_n umefafanuliwa na x_1 115 na x_k x_k - 12 x_k - 1 kwa k zote ge 2. Kokotoafrac1x_1 1 frac1x_2 1 frac1x_3 1 dotsb.  <response>: Zingatia neno frac1x_k - 1 1. Tunaweza kuzidisha nambari na kipunguzo kwa x_k - 1, ili kupatafracx_k - 1x_k - 12 x_k - 1 fracx_k - 1x_k.Ili kupata jumla kwa darubini, tunaweza kuzidisha nambari na denominator tena kwa x_k - 1:fracx_k - 12x_k - 1 x_k fracx_k - x_k - 1x_k - 1 x_k frac1 x_k - 1 - frac1x_k.Kwa hivyo,anzaalignfrac1x_1 1 frac1x_2 1 frac1x_3 1 dotsb left frac1x_1 - frac1x_2 kulia kushoto frac1x_2 - frac1x_3 kulia kushoto frac1x_3 - frac 1x_4 kulia dotsb frac1x_1 frac1115.mwishopanga 