The sum to infinity of the series: 1 + (1/3) + (1/9) + (1/27) + ... is
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Correct Answer: Option D
Explanation:
The series is geometric with common ratio \(\frac{1}{3}\).
\(S_{\infty} = \frac{a}{1 - r}\)
= \(\frac{1}{1 - \frac{1}{3}} \)
= \(\frac{1}{\frac{2}{3}}\)
= \(\frac{3}{2}\)
The series is geometric with common ratio \(\frac{1}{3}\).
\(S_{\infty} = \frac{a}{1 - r}\)
= \(\frac{1}{1 - \frac{1}{3}} \)
= \(\frac{1}{\frac{2}{3}}\)
= \(\frac{3}{2}\)