<prompt> Bainisha thamani ya jumla isiyo na kikomosum_n 17infty fracbinomn15binomn17.  <response>: Tuna hiyofracbinomn15binomn17 fracfracn!15! n - 15!fracn!17! n - 17! frac17! n - 17!15! n - 15! frac17 cdot 16n - 15n - 16.Kwa sehemu ndogo,frac1n - 15n - 16 frac1n - 16 - frac1n - 15.Pia tunaweza kuona kwambafrac1n - 15n - 16 fracn - 15 - n - 16n - 15n - 16 frac 1n - 16 - frac1n - 15.Kwa hivyo,anzaalignsum_n 17infty fracbinomn15binomn17 272 sum_n 17infty frac1 n - 15n - 16 272 sum_n 17infty kushoto frac1n - 16 - frac1n - 15 kulia 272 kushoto kushoto 1 - frac12 kulia kushoto frac12 - frac13 kulia kushoto frac13 - frac14 kulia dotsb kulia 272.mwishopanga 