Does the infinite geometric series converge or diverge? 1 + 7/5 + 49/25 + 343/125 + 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. Using the second term (7/5) and the first term (1), we calculate the common ratio (r) as follows: r = (7/5) / 1 = 7/5Find absolute value: Find the absolute value of the common ratio. |r| = |7/5| = 7/5Determine convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio. Since |r| = 7/5 > 1, the series diverges.

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Does the infinite geometric series converge or diverge? $\newline$ $1 + \frac{7}{5} + \frac{49}{25} + \frac{343}{125} + \ldots$ $\newline$ 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{7}{5} + \frac{49}{25} + \frac{343}{125} + \ldots

\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. $\newline$ Using the second term $(\frac{7}{5})$ and the first term $(1)$ , we calculate the common ratio $(r)$ as follows: $\newline$ $r = \frac{\left(\frac{7}{5}\right)}{1} = \frac{7}{5}$
Find absolute value: Find the absolute value of the common ratio. $|r| = |\frac{7}{5}| = \frac{7}{5}$
Determine convergence: Determine if the given geometric series converges or diverges based on the absolute value of the common ratio. $\newline$ Since |r| = \frac{7}{5} > 1, the series diverges.