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A circular flower bed is 24m in diameter and has a circular sidewalk around it that is 2m wide. Find the area of the sidewalk in
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The given series is conditionally convergent. This can be obtained by using alternating series test first and then comparing the series to the harmonic series.
<h3>Determine if diverges, converges, or converges conditionally:</h3>Initially we need to know what Absolute convergence and Conditional convergence,
If → converges, and
→ converges, then the series is Absolute convergence
If → diverges, and
→ converges, then the series is Conditional convergence
First use alternating series test,
=
= 0,
The series is a positive, decreasing sequence that converges to 0.
Next by comparing the series to harmonic series,
≈
= 0
This implies that the series is divergent by comparison to the harmonic series.
First we got that the series is converging and then we got the series is divergent. Therefore the series is conditionally convergent.
→ diverges, and
→ converges, then the series is Conditional convergence.
Hence the given series is conditionally convergent.
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