Does the infinite geometric series converge or diverge? 1 + 5 + 25 + 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. Second term 5 divided by the first term 1 gives the common ratio r. r = 5/1 r = 5Absolute Value: Determine the absolute value of the common ratio. |r| = |5| |r| = 5Check Convergence: Check if the absolute value of the common ratio is less than 1 to determine if the series converges. Since |r| = 5, which is greater than 1, the series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + 5 + 25 + 125 + \dots$ $\newline$ 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 + 5 + 25 + 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 its preceding term. $\newline$ Second term $5$ divided by the first term $1$ gives the common ratio $r$ . $\newline$ $r = \frac{5}{1}$ $\newline$ $r = 5$
Absolute Value: Determine the absolute value of the common ratio. $\newline$ $|r| = |5|$ $\newline$ $|r| = 5$
Check Convergence: Check if the absolute value of the common ratio is less than $1$ to determine if the series converges. $\newline$ Since $|r| = 5$ , which is greater than $1$ , the series diverges.