Extension: Finite Telescoping Sums and Products
Read this topicExplanations 5
- Telescoping sums (or telescoping series) are series whose partial sums eventually cancel each other out to leave certain initial and final terms. The name arises from older tele…
By Bill Zhang, Ritesh Ragavender, Agnishom Chattopadhyay, Victor Wang, Ruiran Xun, Anusha Rahman
- Telescoping sums are series whose terms will stack together and cancel themselves out. Just like the telescopes that some pirates used, the telescopes that these sums were named…
By Brandon W, Ray Li, Zach Sekaran, Victor Wang, Ruiran Xun, Anusha Rahman
- ####Practice Questions Telescoping sums are sums wherein terms cancel out each other, leaving only a few terms. There are various techniques used to simplify telescoping sums. L…
By Farrell Eldrian Wu, Ryan Alweiss, Anusha Rahman
- (Video) Telescoping Series by patrickJMT In this video, patrickJMT walks you through an example of finding the sum of a telescoping series, using partial fractions.
By Anusha Rahman
- Telescoping Sums and Products A telescoping sum is a sum in which many of the terms cancel each other out. Instead of adding every term separately, you look for terms that appea…
By Anusha Rahman
Problems 4
- For a permutation π\piπ of the integers from 111 to 101010, define S(π)=∑i=19(π(i)−π(i+1))⋅(4+π(i)+π(i+1)),S(\pi) = \sum_{i=1}^{9} (\pi(i) - \pi(i+1))\cdot (4 + \pi(i) + \pi(i+1…
- Simplify the expression 32⋅43⋅54⋯20162015.\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdots\frac{2016}{2015}.23⋅34⋅45⋯20152016.
- Evaluate the sum 12+16+112+⋯+1420\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\cdots+\frac{1}{420}21+61+121+⋯+4201 as a fraction in simplest form.
- Evaluate the sum ∑n=12019ln(n+1n).\sum^{2019}_{n = 1}\ln\left(\frac{n + 1}{n}\right).n=1∑2019ln(nn+1).