Infinite geometric series

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. If −1<r<1-1 < r < 1 , an infinite series is convergent:
    S∞= S_{\infty} = t11−r \large\frac{t_1}{1-r}

    Otherwise, an infinite series is divergent:
    S∞= S_{\infty} = undefined
?
Examples
Lessons
  1. Using the common ratio to determine whether a sum to infinity exists
    For each geometric series determine the:
    i) common ratio.
    ii) sum of the first 10 terms.
    iii) sum to infinity.
    1. 4 + 2 + 1 + …
    2. 2 - 10 + 50 - …
    3. −92 -\frac{9}{2} + 3 - 2 + …
  2. Expressing a repeating decimal as an infinite geometric series
    For the repeating decimal:
    i) express it as an infinite geometric series.
    ii) write it as a fraction by evaluating the sum of the infinite geometric series.
    1. 0.461‾0.\overline{461}
    2. 5.123‾5.1\overline{23}
Topic Notes
?
We know how to deal with geometric series with finite terms. But what if we have a series of infinite number of terms? In this section, we will explore the concept behind infinite geometric series, as well as learning how to determine whether an infinite geometric series is convergent or divergent. Just like all other series, we have a formula to help us find the sum to infinity.
Basic Concepts
?
Related Concepts
?