All Precalculus Resources
Example Questions
Example Question #31 : Sequences And Series
What is the 10th term in the series:
1, 5, 9, 13, 17....
37
23
41
45
31
37
The pattern in this arithmetic series is that each term is created by adding 4 to the previous one. You can then continue the series by continuing to add 4s until you've gotten to the tenth term:
1, 5, 9, 13, 17, 21, 25, 29, 33, 37
The correct answer, then, is 37.
Example Question #1 : Partial Sums Of Series
For the sequence
Determine .
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 #2 : Partial Sums Of Series
Simplify the sum.
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 #3 : Partial Sums Of Series
In case you are not familiar with summation notation, note that:
Given the series above, what is the value of ?
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 #1 : Partial Sums Of Series
In case you are not familiar with summation notation, note that:
What is the value of ?
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,
Example Question #1 : Sums Of Infinite Series
Find the value for
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 #41 : Pre Calculus
Evaluate:
The series does not converge.
This is a geometric series whose first term is and whose common ratio is . The sum of this series is:
Example Question #2 : Sums Of Infinite Series
Evaluate:
The series does not converge.
This is a geometric series whose first term is and whose common ratio is . The sum of this series is:
Example Question #1 : Sums Of Infinite Series
What is the sum of the following infinite series?
diverges
This series is not alternating - it is the mixture of two geometric series.
The first series has the positive terms.
The second series has the negative terms.
The sum of these values is 3.5.
Example Question #3 : Sums Of Infinite Series
What is the sum of the alternating series below?
The alternating series follows a geometric pattern.
We can evaluate the geometric series from the formula.