<prompt> Acha F_n iwe mfuatano wa Fibonacci, yaani, F_0 0, F_1 1, na F_n2 F_n1 F_n. Kokotasum_n0infty fracF_n10n.  <response>: Acha S sum_n 0infty fracF_n10n. KishaanzaalignS F_0 fracF_110 fracF_2102 fracF_3103 dotsb fracF_0 110 fracF_1 F_0102 fracF_2 F_1103 dotsb frac110 fracF_010 fracF_1102 fracF_2103 dotsb fracF_0 102 fracF_1103 dotsb frac110 frac110 S frac1102 S.endalignKutatua, tunapata S frac1089. 