<prompt> Hebu omega e2 pi i1729. Ihesabusum_k 11728 frac11 omegak omega2k omega3k.  <response>: Kwa kuwa 1 omegak omega2k omega3k na uwiano wa kawaida omegak neq 1, tunaweza kuandikafrac11 omegak omega2k omega3k frac1 - omegak1 - omega4k .Kwa kuwa omega1729 e2 pi i 1,omegak omegak cdot omega17293k omega5188k,hivyoanzaalignfrac1 - omegak1 - omega4k frac1 - omega5188k1 - omega4k 1 omega4k omega8k nukta omega5184k jumla_j 01296 omega4jk.mwishoalignKwa hiyo,anzaalignjumla_k 11728 frac11 omegak omega2k omega3k sum_k 11728 jumla_j 01296 omega4jk jumla_j 01296 jumla_k 11728 omega4jk 1728 sum_j 11296 jumla_k 11728 omega4jk 1728 sum_j 11296 omega4j omega8j nukta omega4 cdot 1728j 1728 sum_j 11296 omega4j 1 omega4j dots omega4 cdot 1727j 1728 sum_j 11296 omega4j cdot frac1 - omega4 cdot 1728j1 - omega4j 1728 sum_j 11296 fracomega4j - omega4 cdot 1729j1 - omega4j 1728 sum_j 11296 fracomega4j - 11 - omega4j 1728 sum_j 11296 -1 1728 - 1296 432.mwishopanga 