1. Oblicz sumę n początkowych wyrazów ciągu geometrycznego (a,,) o ilorazie q  a) [latex]a _{1} =-1,q=2,n=8 [/latex] b) [latex]a _{1} =3,q=- sqrt{2},n=10 [/latex]

[latex]S_{n}=a_{1}cdot frac{1-q^n}{1-q}\ \ a)\ S_{8}=-1cdot frac{1-2^8}{1-2}=-1cdotfrac{1-256}{-1}=-255\ \ b)\ S_{10}=3cdot frac{1-(-sqrt{2})^{10}}{1-(-sqrt{2})}=3cdot frac{1-32}{1+sqrt{2}}=-frac{93}{1+sqrt{2}}=-frac{93(1-sqrt{2})}{(1+sqrt{2})(1-sqrt{2})}=\ \=-frac{93(1-sqrt{2})}{-1}=93(1-sqrt{2})[/latex]