We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Sigma Notation

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 Next →

Example Question #1 : Sigma Notation

$\sum_{n=1}^{5}2n-3$

What is the sum of the series?

Possible Answers:

Correct answer:

Explanation:

$\sum_{n=1}^{5}2n-3$

The number on the bottom is the first value we plug in for n. We keep substituting higher and higher integer values of n until we get to the top number (in this case, 5).

Here's what it looks like:

[2(1)-3]+[2(2)-3]+[2(3)-3]+[2(4)-3]+[2(5)-3]

[2-3]+[4-3]+[6-3]+[8-3]+[10-3]

-1+1+3+5+7

Report an Error

Example Question #2 : Sigma Notation

$\sum_{n=1}^{\infty }\frac{1}{2^n}$

What is the sum of the series?

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Recall the formula for the sum of an infinite geometric series:

$S = \frac{a}{1-r}$

Of course, this formula only works if the series is geometric with a common ratio between -1 and 1.

While the sigma notation calls for substituting an infinite number of values for n, let's just substitute a few to see if we can find a pattern:

$\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...$

$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...$

From this, we can see that we have a geometric series with a common ratio of 1/2 and a first term of 1/2.

$S = \frac{\frac{1}{2}}{1-\frac{1}{2}}=\frac{\frac{1}{2}}{\frac{1}{2}}=1$

Report an Error

Example Question #3 : Sigma Notation

Solve for if $x = \sum i^{2}$ for i = 1 to i = 5

Possible Answers:

Correct answer:

Explanation:

For summations, we evaluate the expression at each value of , then add all of the results together.

For this problem, we are working from i = 1 to i = 5 .

i = 1 : i^2 = 1

i = 2 : 2^2=4

i = 3 : 3^2=9

i = 4 : 4^2=16

i = 5 : 5^2=25

Then adding everything up, we get 1 + 4 + 9 + 16 + 25 = 55

Report an Error

Example Question #1 : Sigma Notation

Evaluate the following summation:

$\sum_{n=1}^{5}\frac{n^2+4}{2n}$

Possible Answers:

$\frac{79}{16}$

$\frac{211}{42}$

$\frac{29}{10}$

$\frac{181}{15}$

$\frac{4}{3}$

Correct answer:

$\frac{181}{15}$

Explanation:

According to the notation in the problem, we are told to sum the results obtained by evaluating the equation at each integer between the numbers below and above the sigma. For the sigma notation of this problem in particular, this means we start by plugging 1 into our equation, and then add the results obtained from plugging in 2, and then 3, and then 4, stopping after we add the result obatined from plugging 5 into the equation, as this is the number on top of sigma at which we stop the summation. This process is worked out below:

$\sum_{n=1}^{5}\frac{n^2+4}{2n}=\frac{1^2+4}{2(1)}+\frac{2^2+4}{2(2)}+\frac{3^2+4}{2(3)}+\frac{4^2+4}{2(4)}+\frac{5^2+4}{2(5)}$

$=\frac{5}{2}+2+\frac{13}{6}+\frac{5}{2}+\frac{29}{10}=\frac{75}{30}+\frac{60}{30}+\frac{65}{30}+\frac{75}{30}+\frac{87}{30}$

$=\frac{362}{30}=\frac{181}{15}$

Report an Error

Example Question #5 : Sigma Notation

Evaluate: $\sum_{n=1}^{5} n$

Possible Answers:

120

Correct answer:

Explanation:

The summation starts from 1 and ends at 5. This can be rewritten as:

$\sum_{n=1}^{5} n =1+2+3+4+5=15$

Report an Error

Example Question #6 : Sigma Notation

Evaluate: $\sum_{n=1}^{5} n^2$

Possible Answers:

14400

225

Correct answer:

Explanation:

The summation starts from 1 and ends at 5. Rewrite the summation sign:

$\sum_{n=1}^{5} n^2=1^2+2^2+3^2+4^2+5^2= 1+4+9+16+25=55$

Report an Error

Example Question #7 : Sigma Notation

Evaluate: $\sum_{n=1}^{5} (-1)^n (2^n)$

Possible Answers:

Correct answer:

Explanation:

Rewrite the summation starting from 1 to 5 and add the terms.

$\sum_{n=1}^{5} (-1)^n (2^n)=$

(-1)^1 (2^1)+(-1)^2 (2^2)+(-1)^3 (2^3)+(-1)^4 (2^4)+(-1)^5 (2^5)

=-2+4-8+16-32

=-22

Report an Error

Example Question #1 : Sigma Notation

Evaluate: $\sum_{n=0}^{3} \ln(n)$

Possible Answers:

$\ln(9)$

e^6

$\ln(7)$

$\text{Does not exist}$

$\ln(2)+\ln(3)$

Correct answer:

$\text{Does not exist}$

Explanation:

The natural log domain is only valid for values greater than zero. Therefore, the solution does not exist.

Report an Error

Example Question #31 : Mathematical Relationships And Basic Graphs

The Fibonacci sequence is given as

a_1=1

a_2=1

a_3=2

a_4=3

a_5=5

a_6=8

a_7=13

Find

$\sum_{i=1}^{4}a_i$ .

Possible Answers:

Correct answer:

Explanation:

$\sum_{i=1}^{4}a_i$ is defined to be the sum of the a_i terms from $1\leq i\leq 4$ for $i\epsilon \mathbb{Z}$ .

In other words,

$\\ \sum_{i=1}^{4}a_i \\ \\= a_1+a_2+a_3+a_4\\ \\=1+1+2+3\\ \\=7$

As such, the asnwer is .

Report an Error

Example Question #32 : Mathematical Relationships And Basic Graphs

Calculate: $\sum_{1}^{4} n+2$

Possible Answers:

Correct answer:

Explanation:

The sigma notation indicates summation starting from 1 and ends at 4.

Substitute in order of the iteration.

$\sum_{1}^{4} n+2$

= (1+2)+(2+2)+(3+2)+(4+2)

= 3+4+5+6

$\sum_{1}^{4} n+2 = 18$

The correct answer is .

Report an Error

← Previous 1 2 3 4 Next →

View Algebra 2 Tutors

Nico
Certified Tutor

New York University, Bachelors, Philosophy.

View Algebra 2 Tutors

Hadassah
Certified Tutor

Oakwood University, Bachelor of Science, Mathematics Teacher Education. University of Phoenix-Online Campus, Masters in Educa...

View Algebra 2 Tutors

Emilie
Certified Tutor

Western Governors University, Bachelor of Science, Accounting and Business Management. Western Governors University, Master o...

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Washington DC, SSAT Tutors in Denver, Reading Tutors in San Francisco-Bay Area, SAT Tutors in Houston, Reading Tutors in San Diego, LSAT Tutors in San Francisco-Bay Area, SSAT Tutors in San Francisco-Bay Area, Algebra Tutors in San Francisco-Bay Area, MCAT Tutors in Miami, English Tutors in San Francisco-Bay Area

Popular Courses & Classes

GRE Courses & Classes in Houston, Spanish Courses & Classes in Seattle, MCAT Courses & Classes in Denver, SAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Phoenix, ISEE Courses & Classes in Denver, MCAT Courses & Classes in Atlanta, GRE Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in Chicago

Popular Test Prep

SSAT Test Prep in Philadelphia, SAT Test Prep in Seattle, ISEE Test Prep in New York City, GRE Test Prep in Seattle, GRE Test Prep in Washington DC, SSAT Test Prep in Phoenix, LSAT Test Prep in Houston, SSAT Test Prep in Boston, ACT Test Prep in Denver, ISEE 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

Algebra II : Sigma Notation

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Sigma Notation

Example Question #2 : Sigma Notation

Example Question #3 : Sigma Notation

Example Question #1 : Sigma Notation

Example Question #5 : Sigma Notation

Example Question #6 : Sigma Notation

Example Question #7 : Sigma Notation

Example Question #1 : Sigma Notation

Example Question #31 : Mathematical Relationships And Basic Graphs

Example Question #32 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: