So the identity is actually:\sum_{i = 0}^{n-1} i = \frac{n(n-1)}{2}

Thread starter killerfish
Start date Sep 5, 2009
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identities Summation

In summary, summation identities, also known as sum formulas, are mathematical equations used to simplify and solve complex mathematical expressions by representing the relationship between the sum of a set of numbers and the individual numbers within the set. These identities are widely used in various fields of science, such as statistics, physics, and chemistry, to analyze and interpret data, as well as in mathematical modeling to describe and predict real-world phenomena. The most commonly used summation identity is the arithmetic series formula, which calculates the sum of a finite arithmetic sequence. Summation can be differentiated from integration, where summation is the process of adding a sequence of numbers and integration is the process of finding the area under a curve. Some summation identities can be applied to

Sep 5, 2009

killerfish

Hi guys,

sry if i asked a silly qns. Is the below equivalent is true?

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Sep 5, 2009

jgens

Gold Member

No, that's not correct. Using your limits of summation you should have:

[tex]\sum_{i = 0}^{n-1} i = \frac{n(n-1)}{2}[/tex]

Related to So the identity is actually:\sum_{i = 0}^{n-1} i = \frac{n(n-1)}{2}

1. What are summation identities?

Summation identities, also known as sum formulas, are mathematical equations that represent the relationship between the sum of a set of numbers and the individual numbers within the set. These identities are used to simplify and solve complex mathematical expressions.

2. How are summation identities used in science?

Summation identities are used in various fields of science, such as statistics, physics, and chemistry, to analyze and interpret data. They are also used in mathematical modeling to describe and predict real-world phenomena.

3. What is the most common summation identity?

The most commonly used summation identity is the arithmetic series formula, which calculates the sum of a finite arithmetic sequence. It is given by the formula: Sn = n/2 * (a1 + an), where Sn is the sum of the sequence, n is the number of terms, a1 is the first term, and an is the last term.

4. What is the difference between summation and integration?

Summation is the process of adding a sequence of numbers, while integration is the process of finding the area under a curve. Summation can be thought of as a discrete version of integration, where the individual values are added instead of the infinitesimal values under the curve.

5. Can summation identities be applied to infinite series?

Yes, some summation identities can be applied to infinite series, such as the geometric series formula. However, infinite series can be more complex and require advanced mathematical techniques to solve.