<prompt> Kokotasum_n 1infty frac2n - 1nn 1n 2.  <response>: Kwanza, tuligawanya frac2n - 1nn 1n 2 katika sehemu ndogo kwa kuandika.frac2n - 1nn 1n 2 fracAn fracBn 1 fracCn 2.Kisha 2n - 1 An 1n 2 Bnn 2 Cnn 1.Kuweka n 0, tunapata -1 2A, hivyo A -frac12.Kuweka n -1, tunapata -3 -B, hivyo B 3.Kuweka n -2, tunapata 2C -5, hivyo C -frac52. Hivyo,frac2n - 1nn 1n 2 -frac12n frac3n 1 - frac5 2n 2.Kwa hivyo,anzaalignsum_n 1infty frac2n - 1nn 1n 2 kushoto -frac121 frac 32 - frac523 kulia kushoto -frac122 frac33 - frac52 4 kulia quad left -frac123 frac34 - frac525 kulia kushoto -frac1 24 frac35 - frac526 kulia dotsb -frac12 frac522 frac34.mwishopanga 