### All High School Math Resources

## Example Questions

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

Find the sum of all even integers from to .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

The series does not converge.

**Correct answer:**

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:

**Possible Answers:**

The series does not converge.

**Correct answer:**

This is a geometric series whose first term is and whose common ratio is . The sum of this series is: