Jeśli a1=8 i q=0,5 , to S6 obliczymy z wzoru:
S6=a1(1-q^6)/(1-q)
S6=8·(1-(1/2)^6)/(1-1/2)=16·(1-1/64)=16·63/64=1/4·63=63/4=15 3/4
Odpowiedź:
[tex]S_6} = 15,75[/tex]
Szczegółowe wyjaśnienie:
[tex]a_1 = 8\\q = \frac{1}{2}\\n = 6\\S_{6} = ?[/tex]
[tex]S_{n} = a_1\cdot\frac{1-q^{n}}{1-q}\\\\S_6 = 8\cdot\frac{1-(\frac{1}{2})^{6}}{1-\frac{1}{2}} =8\cdot\frac{1-\frac{1}{64}}{\frac{1}{2}} = 8\cdot\frac{\frac{64}{64}-\frac{1}{64}}{\frac{1}{2}} = 8\cdot\frac{\frac{63}{64}}{\frac{1}{2}} =8\cdot\frac{63}{64}\cdot2 = 16\cdot\frac{63}{64} = \frac{63}{4} = 15,75[/tex]