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:
This also works for finite sums like :
Use 1. to get the decimal representation:
This checks that :
Some functions have an infinite sum representation, and Mathematica will recognize these. For example :
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:
Even more abstract functions will be recognized; the Product representation of involves the set of prime numbers: