Table 4.1.3(a) lists Maple-computed closed-form expressions for sums of , and . The summation symbol is provided by the Expression palette. The Context Panel options Evaluate and Display Inline, and Factor are used to obtain and simplify the results.
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Table 4.1.3(a) Closed-form expressions for sums of powers of the index
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Table 4.1.3(b) contains the Maple calculations for the right Riemann sum and its simplifications. The RiemannSum command from the Student Calculus1 package is used to obtain the sum. (This command is also used in the Riemann Sum task templates.)
Initialize and define the function
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Tools≻Load Package: Student Calculus 1
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Loading Student:-Calculus1
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Write
Context Panel: Define Function
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Obtain the right Riemann sum
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Apply the RiemannSum command and press the Enter key.
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Context Panel: Evaluate Sum
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Context Panel: Simplify≻Simplify
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Table 4.1.3(b) Maple's calculation of the right Riemann sum for on the interval
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The passage from to is effected by using the expressions in Table 4.1.5.