<prompt> Kokotafrac123 - 2 frac133 - 3 frac143 - 4 vidoti frac11 1003 - 100.  <response>: Kwanza, tunatenganisha frac1n3 - n frac1n - 1nn 1 katika sehemu ndogo. Hebufrac1n - 1nn 1 fracAn - 1 fracBn fracCn 1 .Kisha1 Ann 1 Bn - 1n 1 Cnn - 1.Kuweka n 1, tunapata 2A 1, hivyo A frac12.Kuweka n 0, tunapata -B 1, hivyo B -1.Kuweka n -1, tunapata 2C 1, hivyo C frac12. Kwa hivyo,frac1n3 - n frac12n - 1 - frac1n frac12n 1. Kwa hiyo,anzaalignsum_n 2infty frac1n3 - n sum_n 2infty kushoto frac12n - 1 - frac1n frac12n 1 kulia kushoto frac121 - frac12 frac123 kulia kushoto frac12 2 - frac13 frac124 kulia kushoto frac123 - frac14 frac125 kulia quad dots left frac1298 - frac199 frac12100 kulia left frac 1299 - frac1100 frac12101 kulia frac121 - frac122 - frac12100 frac12101 frac504920200.mwishopanga 