<prompt> Kokotasum_n 1infty fracF_n 1F_n F_n 2,ambapo F_n inaashiria nambari ya nth Fibonacci, kwa hivyo F_0 0 na F_1 1.  <response>: Tangu F_n 1 F_n 2 - F_n,fracF_n 1F_n F_n 2 fracF_n 2 - F_nF_n F_n 2 frac1 F_n - frac1F_n 2.Kishaanzaalignsum_n 1infty frac1F_n F_n 2 kushoto frac1F_1 - frac1F_3 kulia kushoto frac1F_2 - frac1F_4 kulia kushoto frac1F_3 - frac1F_5 kulia dotsb frac1F_1 frac1F_2 2.mwishopanga 