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Does the infinite geometric series converge or diverge?\newline1+5+25+125+…1 + 5 + 25 + 125 + \dots\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+5+25+125+…1 + 5 + 25 + 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 its preceding term.\newlineSecond term 55 divided by the first term 11 gives the common ratio rr.\newliner=51r = \frac{5}{1}\newliner=5r = 5
  2. Absolute Value: Determine the absolute value of the common ratio.\newline∣r∣=∣5∣|r| = |5|\newline∣r∣=5|r| = 5
  3. Check Convergence: Check if the absolute value of the common ratio is less than 11 to determine if the series converges.\newlineSince ∣r∣=5|r| = 5, which is greater than 11, the series diverges.

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