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Leg: qquad qquad Hypotenuse: qquad qquad

11.\newlineLeg: \qquad \newline \qquad \newlineHypotenuse: \qquad \newline \qquad

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Convergent and divergent geometric seriesright chevron icon

Full solution

Q. 11.\newlineLeg: \qquad \newline \qquad \newlineHypotenuse: \qquad \newline \qquad
  1. Find common ratio: Find the common ratio rr of the series by dividing the second term by the first term.\newlineCalculation: r=34/1=34r = \frac{3}{4} / 1 = \frac{3}{4}
  2. Check absolute value: Check if the absolute value of the common ratio is less than 11 to determine if the series converges.\newlineCalculation: ∣r∣=∣34∣=34|r| = |\frac{3}{4}| = \frac{3}{4}
  3. Series convergence: Since ∣r∣=34|r| = \frac{3}{4}, which is less than 11, the series converges.

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