algebra
Telescoping — AMC & AIME Problems
52 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Telescoping — a algebra concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: Extension: Finite Telescoping Sums and Products.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 8
AMC 10
AMC 12
- 1957 AMC 12 Problem 5
- 1959 AMC 12 Problem 37
- 1959 AMC 12 Problem 45
- 1971 AMC 12 Problem 32
- 1974 AMC 12 Problem 20
- 1977 AMC 12 Problem 18
- 1977 AMC 12 Problem 24
- 1985 AMC 12 Problem 24
- 2004 AMC 12A Problem 25
- 2005 AMC 12B Problem 13
- 2008 AMC 12A Problem 4
- 2010 AMC 12A Problem 19
- 2012 AMC 12B Problem 25
- 2014 AMC 12A Problem 21
- 2014 AMC 12B Problem 23
- 2016 AMC 12B Problem 21
- 2018 AMC 12B Problem 7
- 2018 AMC 12B Problem 18
- 2019 AMC 12A Problem 23
- 2019 AMC 12B Problem 22
- 2021 AMC 12A Spring Problem 9
- 2025 AMC 12B Problem 7
AIME
- 1987 AIME Problem 14
- 1997 AIME Problem 11
- 1999 AIME Problem 11
- 2000 AIME II Problem 14
- 2000 AIME II Problem 15
- 2002 AIME I Problem 4
- 2002 AIME II Problem 6
- 2003 AIME II Problem 15
- 2005 AIME II Problem 7
- 2006 AIME I Problem 15
- 2008 AIME II Problem 6
- 2008 AIME II Problem 8
- 2009 AIME I Problem 7
- 2014 AIME II Problem 7
- 2015 AIME II Problem 13
- 2025 AIME II Problem 4
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