## Summation Formulas

### In mathematics, summation formulas are used to express the sum of a series of terms in a concise and compact form

In mathematics, summation formulas are used to express the sum of a series of terms in a concise and compact form. They are particularly helpful when dealing with large numbers of terms, as they allow us to represent the sum using a shorter notation.

Here are some common summation formulas:

1. Arithmetic Series:

An arithmetic series is a sequence of numbers in which the difference between consecutive terms remains constant. The sum of an arithmetic series can be calculated using the following formula:

Sn = (n/2)(a + l)

where Sn represents the sum of the series, n is the number of terms, a is the first term, and l is the last term.

2. Geometric Series:

A geometric series is a sequence of numbers in which each term is multiplied by a common ratio to obtain the next term. The sum of a geometric series can be found using the formula:

Sn = a(r^n – 1) / (r – 1)

Here, Sn represents the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

3. Harmonic Series:

The harmonic series is a sequence of numbers in which each term is the reciprocal of a positive integer. The sum of a harmonic series can be given by the formula:

Sn = 1 + 1/2 + 1/3 + … + 1/n = Hn

In this formula, Sn represents the sum of the series up to the nth term.

These are just a few examples of summation formulas. Depending on the nature of the series, there may be other specific formulas or formulas that can be derived to calculate the sum efficiently. Summation notation, commonly represented by the Greek letter sigma (Σ), is often used to denote the sum of a series.

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