Does the infinite geometric series converge or diverge? 1 + 3/4 + 9/16 + 27/64 + ⋯ Choices: [[converge][diverge]]

Find common ratio: Find the common ratio (r) by dividing the second term by the first term. (3/4) / 1 = 3/4 Common ratio (r): 3/4Check absolute value: Check if the absolute value of r is less than 1. |r| = |3/4| = 3/4 Since 3/4 is less than 1, the series might converge.Apply convergence test: Apply the geometric series convergence test. If |r| < 1, then the series converges. |r| = 3/4 < 1, so the series converges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots$ $\newline$ Choices: $\newline$ $\text{[A]converge}$ $\newline$ $\text{[B]diverge}$

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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{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots

\newline

Choices:

\newline

\text{[A]converge}

\newline

\text{[B]diverge}

Find common ratio: Find the common ratio $r$ by dividing the second term by the first term. $\frac{3}{4} / 1 = \frac{3}{4}$ Common ratio $r$ : $\frac{3}{4}$
Check absolute value: Check if the absolute value of $r$ is less than $1$ . $\newline$ $|r| = |\frac{3}{4}| = \frac{3}{4}$ $\newline$ Since $\frac{3}{4}$ is less than $1$ , the series might converge.
Apply convergence test: Apply the geometric series convergence test. $\newline$ If |r| < 1, then the series converges. $\newline$ |r| = \frac{3}{4} < 1, so the series converges.