RE: Can I just say, and I'm just being honest...
August 11, 2018 at 2:16 am
(This post was last modified: August 11, 2018 at 2:19 am by Kernel Sohcahtoa.)
CIJS,
Tonight I read and analyzed a proof of the binomial theorem in Velleman's How To Prove It, and IMO, it is the clearest and most thorough explanation of it that I've seen. His induction proof actually performs a binomial expansion of the terms and uses algebra and identities dealing with factorials to produce the desired result. In every other book that I've seen, the proof never breaks down to an actual binomial expansion of the terms, which makes it harder to see how the factorial identities and algebra come into play, so I'm grateful to Velleman for his clarity. Hence, this is the first time that I have a true appreciation for the theorem and a good understanding of it.
Tonight I read and analyzed a proof of the binomial theorem in Velleman's How To Prove It, and IMO, it is the clearest and most thorough explanation of it that I've seen. His induction proof actually performs a binomial expansion of the terms and uses algebra and identities dealing with factorials to produce the desired result. In every other book that I've seen, the proof never breaks down to an actual binomial expansion of the terms, which makes it harder to see how the factorial identities and algebra come into play, so I'm grateful to Velleman for his clarity. Hence, this is the first time that I have a true appreciation for the theorem and a good understanding of it.