Odpowiedź:
[tex]a_{3}=2\ \ \ \ q=\frac{1}{2}\\\\\\a_{3}=a_{1}*q\\\\2=a_{1}*\frac{1}{2}\ \ /*2\\\\4=a_{1}\\\\a_{1}=4\\\\\\S_{n}=a_{1}*\frac{1-q^n}{1-q}\\\\\\S_{10}=4*\dfrac{1-(\frac{1}{2})^{10}}{1-\frac{1}{2}}=4*\dfrac{1-\frac{1}{1024}}{\frac{1}{2}}=4*\dfrac{\frac{1024}{1024}-\frac{1}{1024}}{\frac{1}{2}}=4*\dfrac{\frac{1023}{1024}}{\frac{1}{2}}=\\\\\\=4*\frac{1023}{1024}:\frac{1}{2}=4*\frac{1023}{1024}*2=\not8^1*\frac{1023}{\not1024_{128}}=\frac{1023}{128}=7\frac{127}{128}\\\\\\S_{10}=7\frac{127}{128}[/tex]
