Does the infinite geometric series converge or diverge? 1 + 8/5 + 64/25 + 512/125 + Choices: (A)converge (B)diverge

Identify Common Ratio: Identify the common ratio of the geometric series by dividing a term by its preceding term. Two consecutive terms are 1 and 8/5. (8/5) / 1 = 8/5 Common Ratio (r): 8/5Find Absolute Value: Find the absolute value of the common ratio. |r| = |8/5| |r| = 8/5Determine Convergence: Determine if the given geometric series converges or diverges. Since |r| = 8/5 > 1, the series diverges because the absolute value of the common ratio is greater than 1.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{8}{5} + \frac{64}{25} + \frac{512}{125} + \dots$ $\newline$ 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{8}{5} + \frac{64}{25} + \frac{512}{125} + \dots

\newline

Choices:

\newline

(A)converge

\newline

(B)diverge

\newline

Identify Common Ratio: Identify the common ratio of the geometric series by dividing a term by its preceding term. $\newline$ Two consecutive terms are $1$ and $\frac{8}{5}$ . $\newline$ $(\frac{8}{5}) / 1 = \frac{8}{5}$ $\newline$ Common Ratio $(r): \frac{8}{5}$
Find Absolute Value: Find the absolute value of the common ratio. $\newline$ |r| = |\frac{$8$}{$5$}|\(\newline|r| = \frac{ $8$ }{ $5$ } $\newline$
Determine Convergence: Determine if the given geometric series converges or diverges. $\newline$ Since |r| = \frac{8}{5} > 1, the series diverges because the absolute value of the common ratio is greater than $1$ .