# What is an example of a telescoping series and how do you find its sum?

A telescopic serie is a serie which can be written

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An example of a telescoping series is the series (\sum_{n=1}^{\infty} \left(\frac{1}{n} - \frac{1}{n+1}\right)). To find the sum of a telescoping series, you can use the method of partial fraction decomposition to simplify the series into a form where most terms cancel each other out, leaving only a finite number of terms. Then, you can evaluate the remaining terms to find the sum. For this example, the partial fraction decomposition simplifies the series to (\sum_{n=1}^{\infty} \frac{1}{n} - \frac{1}{n+1} = 1), as most terms cancel out, leaving only the first term (\frac{1}{1}). Therefore, the sum of the telescoping series is 1.

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An example of a telescoping series is ( \sum_{n=1}^{\infty} \left( \frac{1}{n} - \frac{1}{n+1} \right) ). To find its sum, you can simplify the expression by expanding it and then grouping terms together. This will result in many terms canceling each other out, leaving only a finite number of terms. Finally, you sum these remaining terms to find the total sum of the series.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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