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:
“He who has never failed somewhere, that man can not be great. Failure is the true test of greatness. And if it be said, that continual success is a proof that a man wisely knows his powers,—it is only to be added, that, in that case, he knows them to be small.”
—Herman Melville (1819–1891)
“Every man sees in his relatives, and especially in his cousins, a series of grotesque caricatures of himself.”
—H.L. (Henry Lewis)