Proof
Because we know that for all exists an such that for all we have that, or what is the same
As we can choose such that is positive. So and by the direct comparison test, if converges then so does .
Similarly, so if converges, again by the direct comparison test, so does .
That is both series converge or both series diverge.
Read more about this topic: Limit Comparison Test
Famous quotes containing the word proof:
“The chief contribution of Protestantism to human thought is its massive proof that God is a bore.”
—H.L. (Henry Lewis)
“In the reproof of chance
Lies the true proof of men.”
—William Shakespeare (1564–1616)
“The insatiable thirst for everything which lies beyond, and which life reveals, is the most living proof of our immortality.”
—Charles Baudelaire (1821–1867)