Calculus 2 : Arithmetic and Geometric Series

Study concepts, example questions & explanations for Calculus 2

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Example Questions

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Example Question #201 : Series In Calculus

Calculate the sum, rounded to the nearest integer, of the first 9 terms of the following geometric series: 

Possible Answers:

Correct answer:

Explanation:

This is a geometric series.

The sum of a geometric series can be calculated with the following formula,

, where n is the number of terms to sum up, r is the common ratio, and  is the value of the first term.

We have  and n and we just need to find r before calculating the sum.

Solution:

Example Question #202 : Series In Calculus

Calculate the sum, rounded to the nearest integer, of the first 100 terms of the following geometric series: 

Possible Answers:

Correct answer:

Explanation:

This is a geometric series.

The sum of a geometric series can be calculated with the following formula,

, where n is the number of terms to sum up, r is the common ratio, and  is the value of the first term.

We have  and n and we just need to find r before calculating the sum.

Solution:

Example Question #203 : Series In Calculus

Calculate the sum of the following infinite geometric series:

Possible Answers:

Correct answer:

Explanation:

This is an infinite geometric series.

The sum of an infinite geometric series can be calculated with the following formula,

 , where  is the first value of the summation, and r is the common ratio.

Solution:

Value of  can be found by setting 

r is the value contained in the exponent

Example Question #204 : Series In Calculus

Calculate the sum of a geometric series with the following values:

,, ,

rounded to the nearest integer.

Possible Answers:

Correct answer:

Explanation:

This is a geometric series.

The sum of a geometric series can be calculated with the following formula,

, where n is the number of terms to sum up, r is the common ratio, and  is the value of the first term.

For this question, we are given all of the information we need.

Solution:

Rounding, 

Example Question #205 : Series In Calculus

Calculate the sum of a geometric series with the following values:

, ,

rounded to the nearest integer.

Possible Answers:

Correct answer:

Explanation:

This is a geometric series.

The sum of a geometric series can be calculated with the following formula,

, where n is the number of terms to sum up, r is the common ratio, and  is the value of the first term.

For this question, we are given all of the information we need.

Solution:

Rounding, 

Example Question #2991 : Calculus Ii

Calculate the sum of a geometric series with the following values:

,, ,

rounded to the nearest integer.

Possible Answers:

Correct answer:

Explanation:

This is a geometric series.

The sum of a geometric series can be calculated with the following formula,

, where n is the number of terms to sum up, r is the common ratio, and  is the value of the first term.

For this question, we are given all of the information we need.

Solution:

Rounding, 

Example Question #31 : Types Of Series

Calculate the sum of the following infinite geometric series:

Possible Answers:

Correct answer:

Explanation:

This is an infinite geometric series.

The sum of an infinite geometric series can be calculated with the following formula,

 , where  is the first value of the summation, and r is the common ratio.

Solution:

Value of  can be found by setting 

r is the value contained in the exponent

 

 

Example Question #2993 : Calculus Ii

Calculate the sum of the following infinite geometric series:

Possible Answers:

Correct answer:

Explanation:

This is an infinite geometric series.

The sum of an infinite geometric series can be calculated with the following formula,

 , where  is the first value of the summation, and r is the common ratio.

Solution:

Value of  can be found by setting 

r is the value contained in the exponent

Example Question #2994 : Calculus Ii

Calculate the sum of the following infinite geometric series:

Possible Answers:

Correct answer:

Explanation:

This is an infinite geometric series.

The sum of an infinite geometric series can be calculated with the following formula,

 , where  is the first value of the summation, and r is the common ratio.

Solution:

Value of  can be found by setting 

r is the value contained in the exponent

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