Does the infinite geometric series converge or diverge? 1 + 4/5 + 16/25 + 64/125 + Choices: (A)converge (B)diverge

Identify common ratio: Identify the common ratio of the geometric series by dividing two consecutive terms. The second term is 4/5 and the first term is 1. Common ratio (r) = (4/5) / 1 = 4/5Calculate absolute value: Calculate the absolute value of the common ratio. |r| = |4/5| |r| = 4/5Determine convergence: Determine if the geometric series converges or diverges based on the absolute value of the common ratio. Since |r| = 4/5 < 1, the series converges according to the convergence test for geometric series.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{4}{5} + \frac{16}{25} + \frac{64}{125} + \ldots$ $\newline$ 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{4}{5} + \frac{16}{25} + \frac{64}{125} + \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 second term is $\frac{4}{5}$ and the first term is $1$ . $\newline$ Common ratio $(r) = \frac{\frac{4}{5}}{1} = \frac{4}{5}$
Calculate absolute value: Calculate the absolute value of the common ratio. $\newline$ |r| = |\frac{4}{5}|$\newline|r| = \frac{4}{5}$
Determine convergence: Determine if the geometric series converges or diverges based on the absolute value of the common ratio. $\newline$ Since |r| = \frac{4}{5} < 1, the series converges according to the convergence test for geometric series.