<prompt> Je, ni thamani gani ya jumla ya Ssum_k049-1kbinom992kbinom990-binom99 2binom994-cdots -binom9998?A -250 B -249 C 0 D 249 E 250  <response>: Kwa Nadharia ya Binomial, 1i99sum_n099binom99jin binom990i 0binom991i1binom992i2binom993i3binom994i4 cdots binom9998i98.Kwa kutumia ukweli kwamba i1i, i2-1, i3-i, i41, na in4i n, jumla inakuwa:1i99binom990binom991i-binom992-binom993ibinom 994cdots -binom9998.Kwa hivyo, Re1i99binom990-binom992binom994-cdots -binom99 98 S.Kwa kutumia Nadharia ya De Moivre, 1i99sqrt2cis45circ99sqrt299cdot cis99 cdot45circ249sqrt2cdot cis135circ -249249i.Na hatimaye, SRe-249249i -249. 