<prompt> Hesabu thamani ya mfululizo usio na kikomo sum_n2infty fracn43n210n102n cdoti kushoton44kulia  <response>: Tunahesabu kipunguzo: n44 n222-2n2 n2-2n2n22n2. Sasa,anzaeqnarrayfracn43n210n10n44 1 frac3n210n6n44 1 frac4n2-2n2 - frac1n22n2 Mshale mrefu wa kulia sum_n2infty fracn43n210n102n cdot leftn44kulia sum_n2infty frac12n frac42ncdotn2-2n2 - frac1 2ncdotn22n2 frac12 sum_n2infty frac12n-2cdotleftn-12 1kulia - frac12ncdotleftn121kuliaendeqnarrayMsururu wa darubini za mwisho hadi frac12 frac110; kwa hivyo, jibu letu tunalotaka ni frac12 frac12 frac110 frac1110. 