Why is summation notation important

We will focus solely on understanding summation notation. For the life sciences, it is more important to be able to take a summation notation that has been given to you and know what it means than it is to express a given sum in summation notation. Summation notation is used to compactly represent a sum of numbers. For example, suppose we want to compactly write the following sum,. Sums of numbers, such as the one above, are often called series.

To compactly write the above series, we use the following summation notation,. To understand how this notation represents the above sum, we break the summation notation down into pieces:.

The terms we are going to be summing usually depend on the index of the sum. That is, as the index increments from the lower limit to the upper limit, the terms in the series usually change.

In this case, we are summing the first 15 numbers, so the index itself represents the numbers we are summing. In this case, the index i begins at 0 and ends at 4. We can write out the terms in the summation as i increases from 0 to 4 by substituting each value of i , and then summing the numbers as follows,. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.

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Thus, we have the index values 3, 4, 5, 6, and 7, and the squares of those are 9, 16, 25, 36, and In some cases we may not identify the upper limit of summation with a specific value, instead usingf a variable. Here's an example. The lower limit of summation is 0 and the upper limit is n. Each addend in the sum is found by multiplying the index value by 3 and then adding 1 to that.

Because we do not know the specific value for n, we use an elipsis. Here's the expansion of this summation notation. We may also create sums with an infinite number of addends. In this situation, the upper limit of summation is infinity. There is no last addend, because the upper limit of summation is infinity, indicating we simply continue to create addends following the pattern shown.