Define summation notation and give an example involving a simple series.
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Summation notation, often represented by the Greek letter sigma (Σ), is a concise way to express the sum of a sequence of numbers. It includes an index of summation, a lower bound, an upper bound, and the expression that describes the terms being added together. For example, the summation notation Σ (from i=1 to 5) of i would be written as Σ (i=1 to 5) i, which equals 1 + 2 + 3 + 4 + 5 = 15. Summation notation is not just a mathematical curiosity—it's super handy in various fields! For instance, in statistics, you might use it to calculate the mean of a data set by summing up all the data points and dividing by the number of points. So, if you have test scores of 85, 90, and 78, you'd write it as Σ (i=1 to 3) score_i = 85 + 90 + 78 = 253, before doing your mean calculation!