We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Sequences and Series

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 Next →

Example Question #2 : Finding Partial Sums In A Series

Find the sum of all even integers from to .

Possible Answers:

930

870

990

950

900

Correct answer:

930

Explanation:

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(t_{1}+t_{n})$ ,

where is the number of terms in the series, $t_{1}$ is the first term, and $t_{n}$ is the last term.

$S=\frac{30}{2}(2+60)=15(62)=930$

Report an Error

Example Question #1 : Finding Partial Sums In A Series

Find the sum of the even integers from 250 to 350 .

Possible Answers:

16,000

16,300

15,300

15,500

15,000

Correct answer:

15,300

Explanation:

The sum of even integers represents an arithmetic series.

The formula for the partial sum of an arithmetic series is

$S = \frac{n}{2}(2(a_1)+(n-1)d)$ ,

where a_1 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:

$S = \frac{51}{2}(2(250)+(51-1)2)$

S = 25.5(500+100)

S=15,300

Report an Error

Example Question #1 : Sums Of Infinite Series

Find the value for $\sum_{i=0}^{\infty} (\frac{1}{2})^i$

Possible Answers:

1.25

1.5

Correct answer:

Explanation:

To best understand, let's write out the series. So

$\sum_{i=0}^{\infty} (\frac{1}{2})^i = 1+1/2+(1/2)^2 + (1/2)^3+...+(1/2)^\infty$

We can see this is an infinite geometric series with each successive term being multiplied by $\frac{1}{2}$ .

A definition you may wish to remember is

$1+r+r^2+r^3+... +r^\infty= 1/(1-r)$ where stands for the common ratio between the numbers, which in this case is $\frac{1}{2}$ or . So we get

1/(1-r) = 1/(1-.5) = 1/.5 = 2

Report an Error

Example Question #1 : Sums Of Infinite Series

Evaluate:

$1 + \frac{1}{7} + \frac{1}{49} + \frac{1}{343} +...$

Possible Answers:

$\frac{6}{5}$

$\frac{9}{8}$

$\frac{7}{6}$

The series does not converge.

$\frac{4}{3}$

Correct answer:

$\frac{7}{6}$

Explanation:

This is a geometric series whose first term is $a_{0} = 1$ and whose common ratio is $r = \frac{1}{7}$ . The sum of this series is:

$\frac{a_{0}}{1-r} = \frac{1}{1- \frac{1}{7} } = \frac{1}{\frac{7}{7}- \frac{1}{7}}= \frac{1}{\frac{6}{7}} =\frac{7}{6}$

Report an Error

Example Question #3 : Sums Of Infinite Series

Evaluate:

$1 - \frac{1}{6} + \frac{1}{36} - \frac{1}{216} +...$

Possible Answers:

$\frac{6}{7}$

The series does not converge.

$\frac{2}{3}$

$\frac{4}{5}$

$\frac{7}{8}$

Correct answer:

$\frac{6}{7}$

Explanation:

This is a geometric series whose first term is $a_{0} = 1$ and whose common ratio is $r = - \frac{1}{6}$ . The sum of this series is:

$\frac{a_{0}}{1-r} = \frac{1}{1- \left (- \frac{1}{6} \right )} = \frac{1}{\frac{6}{6}+ \frac{1}{6}}= \frac{1}{\frac{7}{6}} =\frac{6}{7}$

Report an Error

← Previous 1 2 3 Next →

View Tutors

Mauricio
Certified Tutor

Fullerton College, Associate, Maths. University of California, Los Angeles, Bachelor, History.

View Tutors

Saarim
Certified Tutor

St Edwards University, Bachelor of Science, Mathematics.

View Tutors

Michelle
Certified Tutor

University of Rhode Island, Bachelor of Science, Marine Biology. University of Rhode Island, Master of Arts, High School Teac...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

English Tutors in Phoenix, Algebra Tutors in San Diego, MCAT Tutors in Houston, Math Tutors in Dallas Fort Worth, French Tutors in Denver, English Tutors in Seattle, Calculus Tutors in Dallas Fort Worth, English Tutors in Houston, ISEE Tutors in Dallas Fort Worth, SAT Tutors in Phoenix

Popular Courses & Classes

GMAT Courses & Classes in San Diego, SAT Courses & Classes in New York City, SSAT Courses & Classes in Houston, LSAT Courses & Classes in San Diego, GMAT Courses & Classes in Seattle, ACT Courses & Classes in Boston, SSAT Courses & Classes in Boston, ISEE Courses & Classes in Atlanta, ACT Courses & Classes in Houston, LSAT Courses & Classes in Chicago

Popular Test Prep

MCAT Test Prep in San Diego, MCAT Test Prep in Los Angeles, GRE Test Prep in Los Angeles, GMAT Test Prep in Phoenix, ACT Test Prep in Houston, ISEE Test Prep in Phoenix, SSAT Test Prep in Houston, LSAT Test Prep in San Diego, ISEE Test Prep in Atlanta, SSAT Test Prep in Atlanta

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

High School Math : Sequences and Series

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #2 : Finding Partial Sums In A Series

Example Question #1 : Finding Partial Sums In A Series

Example Question #1 : Sums Of Infinite Series

Example Question #1 : Sums Of Infinite Series

Example Question #3 : Sums Of Infinite Series

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: