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

Identify common ratio: Identify the common ratio of the geometric series by comparing two consecutive terms. The first term is 1 and the second term is 2. The common ratio r is obtained by dividing the second term by the first term: r = 2/1 = 2.Determine absolute value: Determine the absolute value of the common ratio. |r| = |2| = 2Check convergence criteria: Check if the absolute value of the common ratio is less than 1 to determine if the series converges. Since |r| = 2 > 1, the series does not meet the convergence criterion for a geometric series.Conclude series status: Conclude whether the series converges or diverges based on the value of |r|. Because |r| > 1, the infinite geometric series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + 2 + 4 + 8 + \ldots$ $\newline$ 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 + 2 + 4 + 8 + \ldots

\newline

Choices:

\newline

(A) converge

\newline

(B) diverge

Identify common ratio: Identify the common ratio of the geometric series by comparing two consecutive terms. $\newline$ The first term is $1$ and the second term is $2$ . $\newline$ The common ratio $r$ is obtained by dividing the second term by the first term: $r = \frac{2}{1} = 2$ .
Determine absolute value: Determine the absolute value of the common ratio. $|r| = |2| = 2$
Check convergence criteria: Check if the absolute value of the common ratio is less than $1$ to determine if the series converges. $\newline$ Since |r| = 2 > 1, the series does not meet the convergence criterion for a geometric series.
Conclude series status: Conclude whether the series converges or diverges based on the value of |r|\. Because \$|r| > 1, the infinite geometric series diverges.