Infinite Geometric Series as Rational Functions
Read this topicExplanations 3
- ####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
- Infinite Geometric Series as Rational Functions An infinite geometric series is a geometric series that goes on forever. Even though the series never ends, it can sometimes be w…
By Anusha Rahman
- Sum of Infinite Geometric Series by Mario's Math Tutoring In this lesson by Mario's Math Tutoring, you will learn how to find the sum of an infinite geometric 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?
- Both multiplication and addition are associative. If we multiply or add an infinite amount of numbers, will the associative property still apply?
- 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?