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Does the infinite geometric series converge or diverge?\newline1+6+36+216+…1 + 6 + 36 + 216 + \ldots\newlineChoices:\newline(A) converge\newline(B) diverge

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Convergent and divergent geometric seriesright chevron icon

Full solution

Q. Does the infinite geometric series converge or diverge?\newline1+6+36+216+…1 + 6 + 36 + 216 + \ldots\newlineChoices:\newline(A) converge\newline(B) diverge
  1. Identify Common Ratio: Identify the common ratio of the geometric series by dividing a term by its preceding term.\newlineCalculation: (61)=6(\frac{6}{1}) = 6\newlineCommon Ratio rr: 66
  2. Calculate Absolute Value: Find the absolute value of the common ratio.\newlineCalculation: ∣r∣=∣6∣=6|r| = |6| = 6
  3. Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio.\newlineSince ∣r∣=6>1|r| = 6 > 1, the series diverges.

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