# High School Math : Sequences and Series

## Example Questions

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### Example Question #2 : Finding Partial Sums In A Series

Find the sum of all even integers from to .      Explanation:

The formula for the sum of an arithmetic series is ,

where is the number of terms in the series, is the first term, and is the last term. ### Example Question #3 : Finding Partial Sums In A Series

Find the sum of the even integers from to .      Explanation:

The sum of even integers represents an arithmetic series.

The formula for the partial sum of an arithmetic series is ,

where is the first value in the series, is the number of terms, and is the difference between sequential terms.

Plugging in our values, we get:   ### Example Question #1 : Sums Of Infinite Series

Find the value for       Explanation:

To best understand, let's write out the series. So We can see this is an infinite geometric series with each successive term being multiplied by .

A definition you may wish to remember is where stands for the common ratio between the numbers, which in this case is or . So we get ### Example Question #2 : Sums Of Infinite Series

Evaluate:   The series does not converge.   Explanation:

This is a geometric series whose first term is and whose common ratio is . The sum of this series is: ### Example Question #3 : Sums Of Infinite Series

Evaluate: The series does not converge.     This is a geometric series whose first term is and whose common ratio is . The sum of this series is:  