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!

0/3
?
Examples
Lessons
  1. Geometric series formula:sn=t1  (rn1)r1{s_n} = \frac{{{t_1}\;\left( {{r^n} - 1} \right)}}{{r - 1}}
    Determine the sum of the first twelve terms of the geometric series: 5 – 10 + 20 – 40 + … .
    1. Geometric series formula: sn=rtnt1r1s_{n}=\frac{r \cdot t_{n}-t_{1}}{r-1}
      Determine the sum of the geometric series: 8 + 2 + 12\frac{1}{2} + …. + 1512\frac{1}{{512}} .
      1. A tennis ball is dropped from the top of a building 15 m high. Each time the ball hits the ground, it bounces back to only 60% of its previous height. What is the total vertical distance the ball has travelled when it hits the ground for the fifth time?
        Topic Notes
        ?
        A geometric series is the sum of a finite number of terms in a geometric sequence. Just like the arithmetic series, we also have geometric series formulas to help us with that.
        The sum of n \, n\, terms of a geometric series:

        Sn=t1(rn1)r1=rtnt1r1\large S_n = \frac{t_1(r^{n}-1)} {r-1} = \frac{r \cdot t_{n} - t_{1}} {r-1}