Option C: The sum of the infinite geometric series is [tex]\frac{15}{2}[/tex]
Explanation:
The sum of infinite geometric series can be determined using the formula,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]
Substituting the values [tex]a=5[/tex] and [tex]r=\frac{1}{3}[/tex] in the above formula, we have,
[tex]S_{\infty}=\frac{5}{1-\frac{1}{3} }[/tex]
Simplifying the denominator by taking LCM.
Thus, we have,
[tex]S_{\infty}=\frac{5}{\frac{2}{3} }[/tex]
Simplifying, we get,
[tex]S_{\infty}=5\times{\frac{3}{2} }[/tex]
Multiplying, we get,
[tex]S_{\infty}={\frac{15}{2} }[/tex]
Thus, the sum of the infinite geometric series is [tex]\frac{15}{2}[/tex]
Hence, Option C is the correct answer.
