How to Solve a Sigma Math Equation


A sigma math equation simply refers to an equation using sigma notation. Sigma notation is the Greek letter "sigma" — which looks a bit like the capital letter "E," with an n on top and an x = (an integer) on the bottom — and is called a Riemann sum. When this notation precedes an equation, it indicates to solve the equation by finding the sum of the equation between x and n. The x is the lower bound of the equation and n is the upper bound of the equation. To solve the Riemann sum of (4 + 5x) from 1 to 6, you must understand the significance of sigma notation.

  • Write out the sigma equation for the equation (4 + 5x) from 1 to 6 by first drawing the symbol for sigma, placing 6 on top of the symbol and writing x = 1 beneath the symbol. This signifies the sum begins with x = 1 and ends with x = 6.

  • Solve the sum by first writing out each equation for the sum. For example, the set of equations for the sum of (4 + 5x) is: (4 + 5 1) + (4 + 5 2) + (4 + 5 3) + (4 + 5 4) + (4 + 5 5) + (4 + 5 6). Begin with x = 1 and end with x = 6.

  • Solve the sum by adding each equation. For example, solving the sum of (4 + 5x) from 1 to 6 works out to be: (4 + 5 1) + (4 + 5 2) + (4 + 5 3) + (4 + 5 4) + (4 + 5 5) + (4 + 5 6) = 9 + 14 + 19 + 24 + 29 + 34 = 129. This is the solution to the sigma equation.

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