Oblicz sumę n początkowych wyrazów ciągu geometrycznego ,jeśli : a)a1= -27 q=1/3 n=5 b)a1= 1/2 q= -1 n=100

a) [latex]S_5= frac{-27 cdot left(( frac{1}{3} )^5-1 ight) }{frac{1}{3}-1}[/latex] [latex]S_5= frac{-27 cdot left(frac{1}{243} -1 ight) }{-frac{2}{3}}[/latex] [latex]S_5= frac{-27 cdot left(-frac{242}{243} ight) }{-frac{2}{3}}[/latex] [latex]S_5= frac{-frac{242}{9} }{-frac{2}{3}}[/latex] [latex]S_5=-frac{121}{3}[/latex] ================ b) [latex]S_{100}= frac{ frac{1}{2} cdot left((-1)^{100}-1 ight) }{-1-1}[/latex] [latex]S_{100}= frac{ frac{1}{2} cdot (1-1)}{-2}[/latex] [latex]S_{100}=0[/latex]