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Summation in mathematics is adding the sequence of numbers, known as summands or addends and the outcome is their total or sum. Apart from numbers, other values are summed too such as matrices, vectors, functions, polynomials, and other elements where the operations are denoted by +.

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What are Summations?

When there is a huge amount of data, you need a sum total of these values. You need summation. Sometimes we have to calculate several terms of any sequence. For writing a large number, a summation notation is helpful. Summation notation can help to write a short form for the addition of huge data sequences.


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Summations are the result when all quantities or numbers are added arithmetically as a sequence. Summation has several terms. These can be two terms or thousand terms, or more. Some might have infinite terms. Summation notation can help to write a short form of an addition of a huge number of data. The symbol signal denotes summation.

Summation Formulas

Summation formulas are used for calculating the sum of sequences. Various kinds of sequences are there including geometric sequence, arithmetic sequence, and others. There are different kinds of summation formulas of various sequences. Summation formulas are there that can find the sum of natural numbers, the sum of cubes of natural numbers, the sum of squares of natural numbers, the sum of odd numbers, the sum of even numbers, and others.

The formulas are given in our Online Writing Services as below:

The formula for the  sum of natural numbers is ∑ni=1i∑i=1ni = 1 + 2 + 3 + ... + n = n(n+1)2

The formula for sum of square numbers is ∑ni=1i2∑i=1ni2 = 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)6

The formula for sum of cubes is ∑ni=1i3∑i=1ni3 = 13 + 23 + 33 + ... + n3 = n2(n+1)24

The formula for sum of even numbers is ∑ni=1∑i=1n 2 i = 2 + 4 + 6 + ... (n numbers) = n (n + 1)

The formula for sum of odd numbers is ∑ni=1∑i=1n (2 i +1) = 1 + 3 + 5 + .... (n numbers) = n2

In a geometric sequence the formula is

he sum of n terms is, ∑ni=1ari−1=a(1−rn)1−r∑i=1nari−1=a(1−rn)1−r and
sum of infinite terms is, ∑∞i=1ari−1=a1−r∑i=1∞ari−1=a1−r (only when |r| < 1)

The general of summation  {x1,x2,…,xn}{x1,x2,…,xn} is denoted by the symbol Σ. i.e., and thus the sum of the sequence = ∑ni=1xi=x1+x2+….xn∑i=1nxi=x1+x2+….xn.


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What are the Uses of Summation?

Mathematical formulae need the addition of multiple variables. Sigma notation or summation is a simple and convenient form of a shorthand that is used for giving a concise expression for the sum of values of variables. It is simply the process or the act of adding. Summation has wide applications and the uses are stated in our Summations Assignment Help

Summation formulas are used for locating the sum of a specific sequence without checking out the sum annually.

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