Does the infinite geometric series converge or diverge? 1 + 6/5 + 36/25 + 216/125 + Choices: (A)converge (B)diverge

Identify Common Ratio: Identify the common ratio of the geometric series by dividing a term by the term before it. 6/5 divided by 1 gives the common ratio (r). r = 6/5Find Absolute Value: Find the absolute value of the common ratio. |r| = |6/5| |r| = 6/5Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio. Since |r| = 6/5 > 1, the series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{6}{5} + \frac{36}{25} + \frac{216}{125} + \dots$ $\newline$ 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{6}{5} + \frac{36}{25} + \frac{216}{125} + \dots

\newline

Choices:

\newline

(A)converge

\newline

(B)diverge

Identify Common Ratio: Identify the common ratio of the geometric series by dividing a term by the term before it. $\frac{6}{5}$ divided by $1$ gives the common ratio $(r)$ . $r = \frac{6}{5}$
Find Absolute Value: Find the absolute value of the common ratio. $\newline$ |r| = |\frac{$6$}{$5$}|\(\newline|r| = \frac{ $6$ }{ $5$ } $\newline$
Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio. $\newline$ Since |r| = \frac{6}{5} > 1, the series diverges.