Does the infinite geometric series converge or diverge? 1 + 3/2 + 9/4 + 27/8 + Choices: (A)converge (B)diverge

Identify Common Ratio: Identify the common ratio of the geometric series by dividing two consecutive terms. The first term is 1 and the second term is 3/2. Common Ratio (r) is calculated as (3/2)/1 = 3/2.Calculate Absolute Value: Determine the absolute value of the common ratio. |r| = |3/2| |r| = 3/2Check Convergence: Check if the absolute value of the common ratio is less than 1 to determine if the series converges. Since |r| = 3/2 > 1, the series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{3}{2} + \frac{9}{4} + \frac{27}{8} + \ldots$ $\newline$ Choices: $\newline$ (A) converge $\newline$ (B) diverge $\newline$

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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?

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1 + \frac{3}{2} + \frac{9}{4} + \frac{27}{8} + \ldots

\newline

Choices:

\newline

(A) converge

\newline

(B) diverge

\newline

Identify Common Ratio: Identify the common ratio of the geometric series by dividing two consecutive terms. $\newline$ The first term is $1$ and the second term is $\frac{3}{2}$ . $\newline$ Common Ratio $(r)$ is calculated as $\frac{\frac{3}{2}}{1} = \frac{3}{2}$ .
Calculate Absolute Value: Determine the absolute value of the common ratio. $|r| = |\frac{3}{2}|$ $|r| = \frac{3}{2}$
Check Convergence: Check if the absolute value of the common ratio is less than $1$ to determine if the series converges. $\newline$ Since |r| = \frac{3}{2} > 1, the series diverges.