Question

Listen Consider the infinite geometric series \( \frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\ldots \) Find the partial sums \( S_{n} \) for \( n=1,2,3,4 \), and 5 . Round to the nearest hundredth. Then describe what happens to \( S_{n} \) as \( n \) increases. \[ S_{1} \approx \] \( \square \) \[ S_{2}= \] \( \square \) \[ S_{3} \approx \] \( \square \) \[ S_{4} \approx \] \( \square \) \[ S_{5} \approx \] \( \square \)

          Listen
Consider the infinite geometric series \( \frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\ldots \) Find the partial sums \( S_{n} \) for \( n=1,2,3,4 \), and 5 . Round to the nearest hundredth. Then describe what happens to \( S_{n} \) as \( n \) increases.
\[
S_{1} \approx
\]
\( \square \)
\[
S_{2}=
\]
\( \square \)
\[
S_{3} \approx
\]
\( \square \)
\[
S_{4} \approx
\]
\( \square \)
\[
S_{5} \approx
\]
\( \square \)

Listen
Consider the infinite geometric series (2)/(3)+(1)/(3)+(1)/(6)+(1)/(12)+(1)/(24)+… Find the partial sums Sn for n=1,2,3,4, and 5 . Round to the nearest hundredth. Then describe what happens to Sn as n increases.

S1≈

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S2=

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S3≈

□

S4≈

□

S5≈

□

Added by Jaime B.

Precalculus Functions and Graphs

Mark Dugopolski 4th Edition

Chapter 11

Instant Answer

Solved by Expert Daniel Pyda

Step 1

The first term \(a\) is \(\frac{2}{3}\), and the common ratio \(r\) can be found by dividing the second term by the first term, which is \(\frac{1}{3} \div \frac{2}{3} = \frac{1}{2}\). Show more…

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Listen Consider the infinite geometric series \( \frac{2}{3}+\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\ldots \) Find the partial sums \( S_{n} \) for \( n=1,2,3,4 \), and 5 . Round to the nearest hundredth. Then describe what happens to \( S_{n} \) as \( n \) increases. \[ S_{1} \approx \] \( \square \) \[ S_{2}= \] \( \square \) \[ S_{3} \approx \] \( \square \) \[ S_{4} \approx \] \( \square \) \[ S_{5} \approx \] \( \square \)