<prompt> Kokotoa sum_a_10inftysum_a_20inftycdotssum_a_70inftydfraca_1a_2cdotsa_73 a_1a_2cdotsa_7.  <response>: Tunaweza kuandika jumla kamajumla_a_1 0infty sum_a_2 0infty dotsb sum_a_7 0infty fraca_1 a_2 dots a_73 a_1 a_2 vitone a_7 jumla_a_1 0infty sum_a_2 0infty dotsb sum_a_7 0infty left fraca_1 3a_1 a_2 vitone a_7 fraca_23a_1 a_2 vitone a_7 vitone fraca_73a_1 a_2 vitone a_7 kulia.Kwa ulinganifu, hii inakunjwa hadi7 jumla_a_1 0infty sum_a_2 0infty dotsb sum_a_7 0infty fraca_13a_1 a_2 dots a_7.Kishaanzaalign7 jumla_a_1 0infty sum_a_2 0infty dotsb sum_a_7 0infty fraca_13a_1 a_2 dots a_7 7 jumla_a_1 0infty sum_a_2 0infty dotsb sum_a_7 0infty left fraca_13a_1 cdot frac13a_2 dotsm frac13a_7 kulia 7 kushoto sum_a 0infty fraca3a kulia left sum_a 0infty frac13 a kulia6.endalignTuna hiyosum_a 0infty frac13a frac11 - 13 frac32.HebuS sum_a 0infty fraca3a frac13 frac232 frac3 33 dotsb.Kisha3S 1 frac23 frac332 frac433 dotsb.Tukiondoa milinganyo hii, tunapata2S 1 frac13 frac132 frac133 dotsb frac32, kwa hivyo S frac34.Kwa hivyo, usemi uliopewa ni sawa na7 cdot frac34 cdot left frac32 kulia6 frac15309256. 