Examples of Convergent and Divergent Series
Read this topicExplanations 4
- ####Background If you need a primer on series in general, check out this explanation. It gives an introduction to what a series is and dips a bit into the ideas of convergent an…
By Ruiran Xun, Anusha Rahman
- Math in Music Now that you've seen the basics of series we are going to dive a little bit deeper into the details by thinking about the musical and mathematical concept known as…
By Jonathan Heller, Deena Hauze, Alex Federspiel, Anusha Rahman
- Examples of Convergent and Divergent Series Not every infinite series behaves the same way. Some infinite series approach a fixed value, while others continue growing or changin…
By Anusha Rahman
- Convergent and Divergent Series In this lesson by the Organic Chemistry Tutor, you will learn the basics of both convergent and divergent series.
By Anusha Rahman
Problems 7
- Does 1+2+3+4+5+...1 + 2 + 3 + 4 + 5 + ...1+2+3+4+5+... converge or diverge?
- Does 1−1+1−1+1+...1 -1 + 1 -1 + 1 + ...1−1+1−1+1+... converge or diverge?
- ∑i=1∞i1000\sum_{i=1}^\infty \frac{i}{1000}i=1∑∞1000i If the above series is convergent, what does it converge to? If not, answer "NO".
- Let {an}\{a_n\}{an} be an infinite sequence defined for n≥1n \ge 1n≥1. Which of the following are true about convergent and divergent series?
- Does the series ∑n=1∞(56)n\sum\limits_{n=1}^{\infty}\left(\frac{5}{6}\right)^nn=1∑∞(65)n converge or diverge?
- Does the series 12+14+16+18+⋯\frac{1}{2} + \frac{1}{4} + \frac{1}{6} + \frac{1}{8} + \cdots21+41+61+81+⋯ converge or diverge?
- Find the value of the series: 1+1+13+24+15+46+17+68+...1 + 1 + \frac{1}{3} + \frac{2}{4} + \frac{1}{5} + \frac{4}{6} + \frac{1}{7} + \frac{6}{8} + ...1+1+31+42+51+64+71+86…