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
Famous quotes containing the words proof and/or series:
“Talk shows are proof that conversation is dead.”
—Mason Cooley (b. 1927)
“Every Age has its own peculiar faith.... Any attempt to translate into facts the mission of one Age with the machinery of another, can only end in an indefinite series of abortive efforts. Defeated by the utter want of proportion between the means and the end, such attempts might produce martyrs, but never lead to victory.”
—Giuseppe Mazzini (1805–1872)