Proof Through 1 / X Series
The series:
Is fairly easy to prove. First, multiply everything by x. On the left side, this makes 1, and on the right side we'll represent x as (x - 1) + 1. Multiply the series by (x - 1) and 1 separately and add the two together.
All terms except 1 cancel out, leaving:
Applying this series to 2 gives:
Read more about this topic: Summation Of Grandi's Series
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