![]() The relative atomic mass, M, of an element consisting of several isotopes (labelled i) will depend on the individual mass, m i, and relative abundance, p i, of each isotope. Steve Strand and Sean Larsen from Portland State University, US, have shown that (pdf), cognitively, the task of interpreting a given summation-notation expression differs significantly from the task of converting a longhand sum into summation notation. Sigma notation is often used to describe sums of combinations of variables, linked by a common label, such as:Īs well as providing shorthand for mathematical ideas, this notation can aid students’ understanding of mathematics. While this variation in notation is potentially confusing, the meaning is usually sufficiently clear from the context. Or one or other of the limits might be omitted altogether, in which case we must rely on the context to define how far the sum should extend. Alternatively, the index might be specified as part of the lower limit, but implied in the upper limit. For example, when there is only a single index that varies through the sum, the index label (in this case, i) might be left out, making it slightly unclear at first glance that i is being incremented rather than x. However, this complete notation is not universally applied, and it is not unusual to see several different variations. Where x i represents a variable x, which can take discrete values labelled by an index variable i. More commonly, the limits refer to labels on the variable. Means ‘add all the values of x from 1 to 5’ orĪdds the squares of these numbers, so thatīy convention, we assume x takes continuous integer values unless otherwise stated. We must therefore include the limits of the summation – the lower limit goes below the sigma and the upper limit above. However, without some definition of the values of x, this is pretty meaningless. The sigma is always combined with another symbol representing the quantities to be added. It is therefore helpful to be able to express the process more concisely.Įighteenth century German mathematician Leonhard Euler introduced the capital Greek letter sigma, Σ, to denote a summation. Summation is one of the earliest operations we meet in mathematics, and it may seem trivial when considering simple addition, such as:īut when more terms are involved, as often happens with applications in chemistry, such sums can become unwieldy. ![]() Source: VanReeel / iStock / Getty Images Plus
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