Does the infinite geometric series converge or diverge? 1 + 12/5 + 144/25 + 1,728/125 + Choices: (A)converge (B)diverge

Identify Common Ratio: Identify the common ratio of the geometric series by dividing a term by its preceding term. We can take the second term (12/5) and divide it by the first term (1). (12/5) / 1 = 12/5Confirm Common Ratio: Now, let's confirm the common ratio by dividing the third term (144/25) by the second term (12/5). (144/25) / (12/5) = (144/25) * (5/12) = 144/60 = 12/5 This confirms that the common ratio (r) is indeed 12/5.Determine Convergence: Determine if the series converges or diverges based on the common ratio. Since the absolute value of the common ratio |r| is |12/5|, which is greater than 1, the series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{12}{5} + \frac{144}{25} + \frac{1,728}{125} + \dots$ $\newline$ Choices: $\newline$ (A) converge $\newline$ (B) diverge

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Math Problems

Algebra 2

Convergent and divergent geometric series

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Q. Does the infinite geometric series converge or diverge?

\newline

1 + \frac{12}{5} + \frac{144}{25} + \frac{1,728}{125} + \dots

\newline

Choices:

\newline

(A) converge

\newline

(B) diverge

Identify Common Ratio: Identify the common ratio of the geometric series by dividing a term by its preceding term. $\newline$ We can take the second term $(\frac{12}{5})$ and divide it by the first term $(1)$ . $\newline$ $\frac{\frac{12}{5}}{1} = \frac{12}{5}$
Confirm Common Ratio: Now, let's confirm the common ratio by dividing the third term $(144/25)$ by the second term $(12/5)$ . $(144/25) / (12/5) = (144/25) \times (5/12) = 144/60 = 12/5$ This confirms that the common ratio $r$ is indeed $12/5$ .
Determine Convergence: Determine if the series converges or diverges based on the common ratio. $\newline$ Since the absolute value of the common ratio |r|$\newline) is |\frac{\(12$}{$5$}|\(\newline), which is greater than \(1 $\newline$ ), the series diverges.