Does the infinite geometric series converge or diverge? 1 + 5/2 + 25/4 + 125/8 + 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 5/2. To find the common ratio (r), divide the second term by the first term: (5/2) / 1 = 5/2. Common Ratio (r): 5/2Calculate Absolute Value: Calculate the absolute value of the common ratio. |r| = |5/2| |r| = 5/2Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio. Since |r| = 5/2 > 1, the series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{5}{2} + \frac{25}{4} + \frac{125}{8} + \ldots$ $\newline$ 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{5}{2} + \frac{25}{4} + \frac{125}{8} + \ldots

\newline

Choices:

\newline

(A) converge

\newline

(B) diverge

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 $\frac{5}{2}$ . $\newline$ To find the common ratio $(r)$ , divide the second term by the first term: $\left(\frac{5}{2}\right) / 1 = \frac{5}{2}$ . $\newline$ Common Ratio $(r)$ : $\frac{5}{2}$
Calculate Absolute Value: Calculate the absolute value of the common ratio. $\newline$ |r| = |\frac{$5$}{$2$}|\(\newline|r| = \frac{ $5$ }{ $2$ } $\newline$ )
Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio. $\newline$ Since |r| = \frac{5}{2} > 1, the series diverges.