What are Special Series?
Special series in mathematics refers to specific sequences of numbers or terms that follow a particular pattern or rule and are widely studied for their unique properties and applications. These series include well-known examples like the arithmetic series, geometric series, harmonic series, and Fibonacci series.
Special Series in Maths – Sequences and Series | Class 11 Maths
Special Series: A series can be defined as the sum of all the numbers of the given sequence. The sequences are finite as well as infinite. In the same way, the series can also be finite or infinite. For example, consider a sequence as 1, 3, 5, 7, … Then the series of these terms will be 1 + 3 + 5 + 7 + ….. The series special in some way or the other is called a special series. The following are the three types of special series.
- 1 + 2 + 3 +… + n (sum of first n natural numbers)
- 12 + 22 + 32 +… + n2 (sum of squares of the first n natural numbers)
- 13 + 23 + 33 +… + n3 (sum of cubes of the first n natural numbers)
In this article, we will read about special series in maths and how to get the formula for all these series. We will also see solved examples and practice problems on special series.
Table of Content
- What are Special Series?
- Special Series 1: Sum of first n natural numbers
- Example on Sum of first n natural numbers
- Special Series 2: Sum of squares of the first n natural numbers
- Examples on Sum of squares of the first n natural numbers
- Special Series 3: Sum of cubes of the first n natural numbers
- Example on Sum of cubes of the first n natural numbers
- Practice Problems on Special Series