We can begin by substituting the terms for k k and listing out the terms of this series.Īt a new job, an employee’s starting salary is $32,100. If we interpret the given notation, we see that it asks us to find the sum of the terms in the series a k = 2 k a k = 2 k for k = 1 k = 1 through k = 5. The number above the sigma, called the upper limit of summation, is the number used to generate the last term in a series. The index of summation is set equal to the lower limit of summation, which is the number used to generate the first term in the series. A variable called the index of summation is written below the sigma. An explicit formula for each term of the series is given to the right of the sigma. Summation notation includes an explicit formula and specifies the first and last terms in the series. Summation notation is often known as sigma notation because it uses the Greek capital letter sigma, Σ, Σ, to represent the sum. Summation notation is used to represent series. Consider, for example, the following series. The sum of the terms of a sequence is called a series. To find the total amount of money in the college fund and the sum of the amounts deposited, we need to add the amounts deposited each month and the amounts earned monthly. To do so, we need to consider the amount of money invested and the amount of interest earned. How much money will they have saved when their daughter is ready to start college in 6 years? In this section, we will learn how to answer this question. The fund pays 6% annual interest, compounded monthly. They plan to invest $50 in the fund each month.
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