?Determine whether the geometric series is convergent or divergent. If it is convergent

Chapter 9, Problem 29

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QUESTION:

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum

\(\sum_{n=1}^{\infty} \frac{(-3)^{n-1}}{4^n}\)

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QUESTION:

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum

\(\sum_{n=1}^{\infty} \frac{(-3)^{n-1}}{4^n}\)

ANSWER:

Step 1 of 2

When the series is written in this form, we can transform it a little into the form of a geometric series:

it is easy to notice that it is a geometric series, where  and .

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