Precalculus : Partial Sums of Series

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #24 : Sequences And Series

For the sequence 

Determine  .

Possible Answers:

Correct answer:

Explanation:

 is defined as the sum of the terms  from  to 

Therefore, to get the solution we must add all the entries from  from  to  as follows.

Example Question #1 : Partial Sums Of Series

Simplify the sum.

Possible Answers:

Correct answer:

Explanation:

The answer is . Try this for :

This can be proven more generally using a proof technique called mathematical induction, which you will most likely not learn in high school.

Example Question #2 : Partial Sums Of Series

In case you are not familiar with summation notation, note that: 

Given the series above, what is the value of  ?

Possible Answers:

Correct answer:

Explanation:

Since the upper bound of the iterator is  and the initial value is , we need add one-half, the summand, six times.

This results in the following arithmetic.

Example Question #3 : Partial Sums Of Series

In case you are not familiar with summation notation, note that: 

What is the value of  ?

Possible Answers:

Correct answer:

Explanation:

Because the iterator starts at , we first have a .

Now expanding the summation to show the step by step process involved in answering the question we get,

 

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