Uploaded July 2026 | Updated September 2026, 2 weeks ago
In this video, you’ll master the Difference Formula (Method of Differences) to easily find the sum of complex sequences and series. We begin with a clear introduction to how telescoping terms cancel out, before diving into step-by-step derivations for the sum of squares ($\sum n^2$) and the sum of cubes ($\sum n^3$) of the first $n$ natural numbers. You'll also get a solid breakdown of Sigma notation to confidently read and write summations, concluding with a practical, hands-on example solving the consecutive product series 1.2 + 2.3 + 3.4 + ... + n(n+1).
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
khanacademy.org/math/class-10-algebra-od/xdf6c731a6bbb91d2:arithmetic-progressions?lang=en
Timestamps:
00:00 - Introduction to difference formula
02:18 - Finding sum of squares of first n natural numbers
07:12 - Finding sum of cubes of first n natural numbers
11:02 - Sigma notation
12:33 - Finding the sum of the series 1.2 + 2.3 + 3.4...+ n(n+1)
Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month.
Support Us: india.khanacademy.org/donate
In this video, you’ll master the Difference Formula (Method of Differences) to easily find the sum of complex sequences and series. We begin with a clear introduction to how telescoping terms cancel out, before diving into step-by-step derivations for the sum of squares ($\sum n^2$) and the sum of cubes ($\sum n^3$) of the first $n$ natural numbers. You'll also get a solid breakdown of Sigma notation to confidently read and write summations, concluding with a practical, hands-on example solving the consecutive product series 1.2 + 2.3 + 3.4 + ... + n(n+1).
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now!
khanacademy.org/math/class-10-algebra-od/xdf6c731a6bbb91d2:arithmetic-progressions?lang=en
Timestamps:
00:00 - Introduction to difference formula
02:18 - Finding sum of squares of first n natural numbers
07:12 - Finding sum of cubes of first n natural numbers
11:02 - Sigma notation
12:33 - Finding the sum of the series 1.2 + 2.3 + 3.4...+ n(n+1)
Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month.
Support Us: india.khanacademy.org/donate
