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Does the infinite geometric series converge or diverge?\newline1+65+3625+216125+…1 + \frac{6}{5} + \frac{36}{25} + \frac{216}{125} + \dots\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+65+3625+216125+…1 + \frac{6}{5} + \frac{36}{25} + \frac{216}{125} + \dots\newlineChoices:\newline(A)converge\newline(B)diverge
  1. Identify Common Ratio: Identify the common ratio of the geometric series by dividing a term by the term before it. 65\frac{6}{5} divided by 11 gives the common ratio (r)(r). r=65r = \frac{6}{5}
  2. Find Absolute Value: Find the absolute value of the common ratio.\newline|r| = |\frac{\(6\)}{\(5\)}|\(\newline|r| = \frac{66}{55}\newline
  3. Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio.\newlineSince ∣r∣=65>1|r| = \frac{6}{5} > 1, the series diverges.

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