<prompt> Kokotoa 1cdot 222cdot 323cdot42cdots19cdot 202.  <response>: Ninaona muundo katika masharti ya jumla hii: kila neno ni la umbo ncdotn12, ambapo n huenda kutoka 1 hadi 19. Ninagundua kuwa n1 2n22n1, ili niweze kuandika upya kila neno kama ncdotn12ncdotn22n1n3 2n2n. Hii ina maana kwamba jumla ni sawa na sum_n119n32n2n. Nakumbuka kwamba sum_ n1k n3frack2k124, sum_n1k n2frackk 12k16, na sum_n1k nfrackk12. Inachomeka k19, Ninapata sum_n119 n3frac192202436100,sum_n1 19 n2frac19203962470, na sum_n119 nfrac1920 2190. Kwa hivyo, jumla ninayotaka kujumlisha ni sum_n119n32n2nsum_n1 19 n32sum_n119 n2sum_n119 n361002cdot 2470190. Kurahisisha, napata 36100494019041230. 