In order to solve this summation, substitute the bottom value of to the function, plus every integer until the iteration reaches to 5.

First, we must identify a pattern in this sum. Note that the sum can be rewritten as:

If we want to start our sum at k=1, then the function must be:

so that the first value is .

In order to finish at , the last k value must be 29 because 29-1=28.

Thus, our summation notation is as follows:

To write in sigma notation, let's make sure we have an alternating sign expression given by:

Now that we have the alternating sign, let's establish a function that increases by per term starting at . This is given by

Putting it all together,

The summation starts at 2 and ends at 4. Write out the terms and solve.

The answer is:

First, evaluate the sum. We can multiply by -2 last.

The sum

means to add together every value for for an integer value of n from 1 to 5:

Now our final step is to multiply by -2.

In order to evaluate the summation, we must understand what the notation of the expression means:

This sigma notation tells us to sum the values obatined from evaluating the expression at each integer between and including those below and above the sigma. So we're going to start by evaluating the expression at n=1, and then add the value of the expression evaluated at n=2, and so on, until we end by adding the last value of the expression evaluated at n=5. This process is shown mathematically below:

means add the values for starting with for every integer until .

This will look like:

Partial sums (written ) are the first few terms of a sum, so

If you then just take off the last number in that sum you get the and so on.

Rewrite the summation term by term:

To simplfy we get a common denominator of 24.

The summation starts at 6 and ends at 7. Increase the value of after each iteration: