Answer
$\displaystyle \sum_{k=1}^{∞}7(\frac{1}{10})^k=\frac{7}{9}$
Work Step by Step
$\displaystyle \sum_{k=1}^{∞}7(\frac{1}{10})^k=\frac{7}{10}+\frac{7}{100}+\frac{7}{1000}+\frac{7}{10000}+...=0.7+0.07+0.007+0.0007+...=0.7777...=\frac{7}{9}$
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