Deret Geometri Tak Hingga

(A)   5 + 15 + 45 + ...

\(r = \dfrac{15}{5} = 3\)

Karena  \(| r | \geq 1\) maka \(S_{\sim} = \: \sim\)

(B)   27 + 9 + 3 + ...

\(a = 27\) dan \(r = \dfrac{9}{27} = \dfrac{1}{3}\)

\begin{equation*}
\begin{split}
S_{\sim} & = \frac{a}{1 - r} \\\\
S_{\sim} & = \frac{27}{1 - \frac{1}{3}} \\\\
S_{\sim} & = \frac{27}{\frac{2}{3}} \\\\
S_{\sim} & = 40\frac{1}{2}
\end{split}
\end{equation*}

(C)   log 256 + log 16 + log 4 + ...

\begin{equation*}
\begin{split}
& \log 256 + \log 16 + \log 4 + \dotso \\\\
& \log 4^4 + \log 4^2 + \log 4 + \dotso \\\\
& 4 \log 4 + 2 \log 4 + \log 4 + \dotso \\\\
\end{split}
\end{equation*}

\(a = 4 \log 4\) dan \(r = \dfrac{2 \: \log 4}{4 \: \log 4} = \dfrac{1}{2}\)

\begin{equation*}
\begin{split}
S_{\sim} & = \frac{4 \log 4}{1 - \frac{1}{2}} \\\\
S_{\sim} & = \frac{4 \log 4}{\frac{1}{2}} \\\\
S_{\sim} & = 8  \log 4
\end{split}
\end{equation*}