Math Is Fun Forum
Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
You are not logged in.
- Topics: Active | Unanswered
#1 2016-11-09 13:27:02
- evene
- Member
- Registered: 2015-10-18
- Posts: 272
How would you find the r+1 term of a binomial expansion?
Given
Or
If . If b is negative, then the signs of the even terms will change. If n is negative, then the expansion becomes
With the general term represented as
Note that this only works when . I am really confused as to how to prove this. I know how to derive the binomial theorem, and I know the actual binomial theorem, but I am not sure how to get the term like they did.
Last edited by evene (2016-11-09 13:28:55)
Offline
#2 2016-11-10 11:02:44
Re: How would you find the r+1 term of a binomial expansion?
Note that the first sum is a finite sum but the second isn't, so you need to impose a condition like |a| < |b| to guarantee convergence. Also, the binomial theorem can also be extended to all real numbers, not just integers. For a proof, I would recommend induction.
Offline