Use the properties of geometric series to find the sum of the series. For what values of the variable does the series converge to this sum? $$1+z / 2+z^{2} / 4+z^{3} / 8+\cdots$$
Added by Alex R.
Step 1
Using the formula for the sum of a geometric series, we have: $$S=\frac{a}{1-r}=\frac{1}{1-z/2}=\frac{2}{2-z}$$ So the sum of the series is $\frac{2}{2-z}$. To determine the values of $z$ for which the series converges, we need to find the values of $z$ that Show more…
Show all steps
Close
Your feedback will help us improve your experience
Adi S and 78 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use the properties of geometric series to find the sum of the series. For what values of the variable does the series converge to this sum? $$2-4 z+8 z^{2}-16 z^{3}+\cdots$$
Sequences and Series
Geometric Series
Find the sum of the series. For what values of the variable does the series converge to this sum? $$1+z / 2+z^{2} / 4+z^{3} / 8+\cdots$$
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD