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Mathematica HowTo
How to | Evaluate Infinite Sums and Products
In calculus, infinite sums and products can pose a challenge to manipulate by hand. Mathematica can evaluate a huge number of different types of sums and products with ease.
Use Sum to set up the classic sum , with the function to sum over as the first argument. Use Mathematica's usual range notation {variable, minimum, maximum} as the second argument:
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This also works for finite sums like :
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Use 1. to get the decimal representation:
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This checks that :
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Some functions have an infinite sum representation, and Mathematica will recognize these. For example :
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Many functions have product representations as well, and Mathematica will even recognize these.
Use Product to check , a function found by the mathematician Euler. The arguments of Product have the same form as Sum:
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Even more abstract functions will be recognized; the Product representation of TooltipBox[zeta, Zeta](s) involves the set of prime numbers:
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