Does the infinite geometric series converge or diverge? 1 + 13/5 + 169/25 + 2,197/125 + Choices: (A)converge (B)diverge

Identify Common Ratio: Identify the common ratio of the geometric series by dividing the second term by the first term. Calculation: (13/5) / 1 = 13/5 Common Ratio (r): 13/5Calculate Absolute Value: Find the absolute value of the common ratio. Calculation: |r| = |13/5| Absolute value of r: 13/5Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio. Since |r| = 13/5 > 1, the series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{13}{5} + \frac{169}{25} + \frac{2,197}{125} + \ldots$ $\newline$ 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{13}{5} + \frac{169}{25} + \frac{2,197}{125} + \ldots

\newline

Choices:

\newline

(A)converge

\newline

(B)diverge

Identify Common Ratio: Identify the common ratio of the geometric series by dividing the second term by the first term. $\newline$ Calculation: $(\frac{13}{5}) / 1 = \frac{13}{5}$ $\newline$ Common Ratio $r$ : $\frac{13}{5}$
Calculate Absolute Value: Find the absolute value of the common ratio. $\newline$ Calculation: |r| = |\frac{$13$}{$5$}|\(\newlineAbsolute value of r: \frac{ $13$ }{ $5$ }
Determine Convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio. $\newline$ Since |r| = \frac{13}{5} > 1, the series diverges.