# Precalculus : Partial Sums of Series

## Example Questions

### Example Question #1 : Partial Sums Of Series

For the sequence

Determine  .

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 #2 : Partial Sums Of Series

Simplify the sum.

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 #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  ?

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 #4 : Partial Sums Of Series

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

What is the value of  ?

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,