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Does the infinite geometric series converge or diverge?\newline1+135+16925+2,197125+…1 + \frac{13}{5} + \frac{169}{25} + \frac{2,197}{125} + \ldots\newlineChoices:\newline(A)converge\newline(B)diverge

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Convergent and divergent geometric seriesright chevron icon

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Q. Does the infinite geometric series converge or diverge?\newline1+135+16925+2,197125+…1 + \frac{13}{5} + \frac{169}{25} + \frac{2,197}{125} + \ldots\newlineChoices:\newline(A)converge\newline(B)diverge
  1. Identify Common Ratio: Identify the common ratio of the geometric series by dividing the second term by the first term.\newlineCalculation: (135)/1=135(\frac{13}{5}) / 1 = \frac{13}{5}\newlineCommon Ratio rr: 135\frac{13}{5}
  2. Calculate Absolute Value: Find the absolute value of the common ratio.\newlineCalculation: |r| = |\frac{\(13\)}{\(5\)}|\(\newlineAbsolute value of r: \frac{1313}{55}
  3. Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio.\newlineSince ∣r∣=135>1|r| = \frac{13}{5} > 1, the series diverges.

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