Does the infinite geometric series converge or diverge? 1 + 9/4 + 81/16 + 729/64 + Choices: (A)converge (B)diverge

Identify terms and ratio: Identify the first term (a) and the common ratio (r) of the geometric series. The first term is 1. To find the common ratio, divide the second term by the first term: (9/4) / 1 = 9/4.Calculate common ratio: Calculate the absolute value of the common ratio: |r| = |9/4| = 9/4.Determine convergence: Determine if the series converges or diverges. A geometric series converges if the absolute value of the common ratio is less than 1. In this case, |r| = 9/4, which is greater than 1.Series divergence: Since |r| > 1, the series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{9}{4} + \frac{81}{16} + \frac{729}{64} + \ldots$ $\newline$ Choices: $\newline$ (A)converge $\newline$ (B)diverge

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Algebra 2

Convergent and divergent geometric series

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Q. Does the infinite geometric series converge or diverge?

\newline

1 + \frac{9}{4} + \frac{81}{16} + \frac{729}{64} + \ldots

\newline

Choices:

\newline

(A)converge

\newline

(B)diverge

Identify terms and ratio: Identify the first term $a$ and the common ratio $r$ of the geometric series. The first term is $1$ . To find the common ratio, divide the second term by the first term: $(\frac{9}{4}) / 1 = \frac{9}{4}$ .
Calculate common ratio: Calculate the absolute value of the common ratio: $|r| = \left|\frac{9}{4}\right| = \frac{9}{4}$ .
Determine convergence: Determine if the series converges or diverges. A geometric series converges if the absolute value of the common ratio is less than $1$ . In this case, $|r| = \frac{9}{4}$ , which is greater than $1$ .
Series divergence: Since |r| > 1, the series diverges.