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Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

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The expression \$\\sum_{\\var{index}=\\var{a}}^{\\var{b}}\\var{f}(\\var{index})\$ is equivalent to which of the following?

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[[0]]

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$\\var{f}(\\var{a})+\\var{f}(\\var{a+1})+\\var{f}(\\var{a+2})+\\ldots + \\var{f}(\\var{b-2})+ \\var{f}(\\var{b-1})+ \\var{f}(\\var{b})$

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$\\var{f}(\\var{index})+\\var{f}(\\var{index})+\\var{f}(\\var{index})+\\ldots + \\var{f}(\\var{index})+ \\var{f}(\\var{index})+ \\var{f}(\\var{index})$

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$\\var{a}+\\var{a+1}+\\var{a+2}+\\ldots + \\var{b-2}+ \\var{b-1}+ \\var{b}$

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Sigma notation is used to represent a sum.

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In this sum, we are adding up a bunch of terms that look like $\\var{f}(\\var{index})$ each for a different value of the index $\\var{index}$. Notice the sum starts with $\\var{index}=\\var{a}$ and ends with $\\var{index}=\\var{b}$, therefore, \$\\sum_{\\var{index}=\\var{a}}^{\\var{b}}\\var{f}(\\var{index})=\\var{f}(\\var{a})+\\var{f}(\\var{a+1})+\\var{f}(\\var{a+2})+\\ldots + \\var{f}(\\var{b-2})+ \\var{f}(\\var{b-1})+ \\var{f}(\\var{b}).\$

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The following question is testing whether you understand the Sigma notation used in mathematics.

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