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
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
involves the set of prime numbers:
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