Calculate the sum of infinity of \(1+\frac{1}{3}±\frac{1}{9}+\frac{1}{27}\)
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Correct Answer: Option C
Explanation:
The given sequence is a geometric progression with the first term \( a = 1 \) and common ratio \( r = \frac{1}{3} \).
The formula for the sum to infinity of a geometric series is:
\[
S_\infty = \frac{a}{1 - r}
\]
Substituting the values:
\[
S_\infty = \frac{1}{1 - \frac{1}{3}} = \frac{1}{\frac{2}{3}} = \frac{3}{2} = 1.5
\]
Thus, the sum to infinity is 1.5, so the correct answer is C.
The given sequence is a geometric progression with the first term \( a = 1 \) and common ratio \( r = \frac{1}{3} \).
The formula for the sum to infinity of a geometric series is:
\[
S_\infty = \frac{a}{1 - r}
\]
Substituting the values:
\[
S_\infty = \frac{1}{1 - \frac{1}{3}} = \frac{1}{\frac{2}{3}} = \frac{3}{2} = 1.5
\]
Thus, the sum to infinity is 1.5, so the correct answer is C.