1-3-6-10 Series Formula: A Mathematical Concept
Introduction
The 1-3-6-10 series formula is a mathematical concept used to calculate the sum of a series of numbers. This formula is commonly used in algebra and is a fundamental concept in mathematics. In this article, we will explore the 1-3-6-10 series formula, its applications, and examples.
What is the 1-3-6-10 Series Formula?
The 1-3-6-10 series formula is a method of calculating the sum of a series of numbers. The formula is as follows:
1 + 3 + 6 + 10 + ... + (n(n+1)/2)
where n is the number of terms in the series.
How Does the Formula Work?
The formula works by adding the first term (1) to the second term (3), then adding the result to the third term (6), and so on. The formula can be written in a more concise form as:
∑(n(n+1)/2)
where ∑ denotes the sum of the series.
Examples and Applications
Example 1:
Find the sum of the series: 1 + 3 + 6 + 10 + 15 + 21
Using the 1-3-6-10 series formula, we can calculate the sum as follows:
1 + 3 + 6 + 10 + 15 + 21 = (6(6+1)/2) = 21(7/2) = 73.5
Example 2:
Find the sum of the series: 1 + 3 + 6 + 10 + ... + 100
Using the formula, we can calculate the sum as follows:
1 + 3 + 6 + 10 + ... + 100 = (10(10+1)/2) = 10(11/2) = 55
The 1-3-6-10 series formula has many applications in mathematics, physics, engineering, and computer science. It is used to calculate the sum of a series of numbers, which is essential in many mathematical and scientific problems.
Conclusion
In conclusion, the 1-3-6-10 series formula is a powerful mathematical concept used to calculate the sum of a series of numbers. It is a fundamental concept in mathematics and has many applications in various fields. By understanding this formula, you can solve a wide range of mathematical problems and applications.
