High School Math : Sequences and Series

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #2 : Finding Partial Sums In A Series

Find the sum of all even integers from  to .

Possible Answers:

Correct answer:

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 .

Possible Answers:

Correct answer:

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 

Possible Answers:

Correct answer:

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:

Possible Answers:

The series does not converge.

Correct answer:

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:

Possible Answers:

The series does not converge.

Correct answer:

Explanation:

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

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