Summation Formulas

About Summation Formulas

We shall first review the definition of summation before moving on to formulas. The total of consecutive terms in a sequence is called summation (or sum). Instead of writing the complete total manually, we use the summation notation to write the sum of more terms, say n terms, of a series (a_n).

i.e., a₁+a₂+...+a_n= Summation Formulas

The total of the series is calculated using summation formulas. There are many different types of sequences, such as arithmetic, geometric, and so on, and thus many different types of summation formulas for different sequences. There are also summation formulas for finding the sum of natural numbers, the sum of natural numbers squared, the sum of natural numbers cubes, the sum of even numbers, the sum of odd numbers, and so on. The following is a list of summation formulas. In the next section, we'll go through each of these formulas in depth.

List of Summation Formulas???????

The sum of two numbers is the outcome of adding two numbers, as we all know. If {x₁,x₂,...,x_n} is a series, the sum of its terms is represented by the symbol Σ(sigma). i.e. total of the preceding series = Summation Formulas = x₁+x₂+….x_n.

Here, Summation Formulas

It is written as "sigma I is equal to 1 to n" and represents the sum of the terms in the sequence from the first to the nth term. However, we do not always need to manually add the sum of the sequences to determine the sum. Instead, we utilise the summation formulas below.

Sum of 1^st n natural numbers is calculated using the
formula:
Sum of squares of the first n natural numbers is calculated using the formula:
Sum of cubes of the first n natural numbers is calculated using the formula:
Sum of fourth powers of the first n natural numbers is calculated using the
formula:
Sum of first n even natural numbers is:
Sum of first n odd natural numbers is:
Sum of arithmetic sequence a, a + d, a + 2d, ... , a + (n - 1) d is:
For geometric sequence a, ar, ar², ... , ar^{n - 1},
Sum of the first n terms is,
The sum of the infinite terms is,(only when |r| less than 1)