Question

Kolejne zadanie z matmy

Answer 1

Dane:

[tex]a_1=9[/tex]

[tex]q=\dfrac{1}{3}[/tex]

[tex]n=4[/tex]

Szukane:

[tex]S_4[/tex]

Wzór:

[tex]S_n=a_1\dfrac{1-q^n}{1-q}[/tex]

Rozwiązanie:

[tex]S_4=9\cdot\dfrac{1-\left(\dfrac{1}{3}\right)^4}{1-\dfrac{1}{3}}=9\cdot\dfrac{1-\dfrac{1}{81}}{\dfrac{2}{3}}=9\cdot\dfrac{\dfrac{80}{81}}{\dfrac{2}{3}}=9\cdot\dfrac{80}{81}\cdot\dfrac{3}{2}=1\cdot\dfrac{40}{3}\cdot\dfrac{1}{1}=\dfrac{40}{3}=13\dfrac{1}{3}[/tex]