Calculating x in Equation (1): A Telescopic Sum

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In summary, to calculate x in Equation (1), one must first understand the equation and identify its repeating pattern. A telescopic sum is a mathematical expression that can be simplified by identifying a repeating pattern within it, such as (1+2) + (2+3) + (3+4) + (4+5) + ... + (n-1+n). However, not all equations have a telescopic sum and may require other methods of simplification. Calculating x in Equation (1) can be useful in a variety of scientific and mathematical applications, as it allows for the simplification of complex expressions and can assist in solving problems related to sequences and series. It is also a valuable skill in problem-solving and critical
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From mathhelpforum.com...

$\displaystyle x=\frac{1}{\sqrt{0}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{4}}+...+\frac{1}{\sqrt{2006}+\sqrt{2008}}$ (1)

... what is the value of x?...

The (1) is a telescopic sum...

$\displaystyle x=\frac{\sqrt{2}}{2} + \frac{\sqrt{4}-\sqrt{2}}{2} + \frac{\sqrt{6}-\sqrt{4}}{2}+... + \frac{\sqrt{2008}-\sqrt{2006}}{2}=\frac{\sqrt{2008}}{2}=22.405356502...$ (2)

Kind regards

$\chi$ $\sigma$
 
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Correct.

Of course, ##\dfrac{\sqrt{2008}}{2}=\sqrt{502} ## .
 
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FAQ: Calculating x in Equation (1): A Telescopic Sum

How do you calculate x in Equation (1)?

To calculate x in Equation (1), you first need to understand the equation and its components. Equation (1) is a telescopic sum, which means that it has a repeating pattern that can be simplified. To calculate x, you will need to identify the pattern and then use that to solve for x.

What is a telescopic sum?

A telescopic sum is a mathematical expression that can be simplified by identifying a repeating pattern within it. This allows for the sum to be reduced to a simpler form, making it easier to solve.

Can you give an example of a telescopic sum?

One example of a telescopic sum is the expression (1+2) + (2+3) + (3+4) + (4+5) + ... + (n-1+n). This can be simplified to n^2, making it a telescopic sum.

Do all equations have a telescopic sum?

No, not all equations have a telescopic sum. A telescopic sum only exists when there is a repeating pattern that can be identified and simplified. Equations without a repeating pattern may have other methods of simplification.

How can calculating x in Equation (1) be useful?

Calculating x in Equation (1) can be useful in a variety of scientific and mathematical applications. It allows for the simplification of complex expressions and can help in solving problems related to sequences and series. It is also a useful skill to have in general problem-solving and critical thinking.

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