Express the sum using summation notation.
\[
1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+\cdots+(-1)^{8}\left(\frac{1}{3^{8}}\right)
\]

Complete the sum of the sequence.
\[
\sum_{k=0}^{\square}(\square)^{k}\left(\frac{1}{\square^{k}}\right)
\]

Answer

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Answer

Final Answer: The sum of the series is \(\boxed{0.7500381039475692}\)

Steps

Step 1 ：Express the sum using summation notation: \(\sum_{k=0}^{8}(-1)^{k}\left(\frac{1}{3^{k}}\right)\)

Step 2 ：Complete the sum of the sequence using the formula for the sum of a geometric series.

Step 3 ：Calculate the sum: \(\sum_{k=0}^{8}(-1)^{k}\left(\frac{1}{3^{k}}\right)\)

Step 4 ：Final Answer: The sum of the series is \(\boxed{0.7500381039475692}\)