Quick question about binomial theorem

Click For Summary

Discussion Overview

The discussion revolves around the binomial theorem, specifically the interpretation of the notation used in the formula, particularly the term where n is above k, often represented as nCk. Participants explore whether this notation requires the use of the nCr function on calculators for expanding binomials.

Discussion Character

  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses uncertainty about the notation where n is above k, questioning if it represents nCk and whether the nCr function is necessary for using the binomial theorem.
  • Another participant confirms that the notation indeed represents nCk and provides an expression for it as n!/[(n-k)!n!].
  • A third participant reflects on a test experience, indicating they used the nCr function to expand a degree 5 binomial, believing it was necessary despite thinking the formula might provide coefficients without it.
  • There is a correction regarding a potential typo in the expression for nCk, with one participant asserting it should be n!/[(n-k)!k!].

Areas of Agreement / Disagreement

Participants generally agree that the notation n above k represents nCk. However, there is some uncertainty regarding the necessity of the nCr function for expanding binomials, as one participant believed it might not be needed.

Contextual Notes

There is a noted discrepancy in the expression for nCk, with participants providing different formulations, indicating potential confusion or differing interpretations of the notation.

MadmanMurray
Messages
76
Reaction score
0
I know how to expand binomials with the aid of pascals triangle and also with the aid of the nCr function on the calculator. I'm not quite sure about this formula though
88573eb41d838aef0f39a929f5eba744.png

see the part in the brackets where n is above k. What does that mean? Someone told me that represents nCk. Is that true? Are you supposed to use that nCr function when using the binomial theorem to expand binomials? I was under the impression that the formula worked out the coefficients without using that nCr function.
 
Physics news on Phys.org
yes the part in the brackets where n is above k is nCk
also expressible as
n!/[(n-k)!n!]
 
Thanks a lot. I thought that formula was some complex way of getting the binomial coefficients without using the nCr button on the calculator. On a test I had a question that asked me to expand a degree 5 binomial using the binomial theorem and I was thinking the teacher wouldn't make us waste our time using that nCr button so many times. I used it anyway so I musta got the question right.
 
lurflurf said:
yes the part in the brackets where n is above k is nCk
also expressible as
n!/[(n-k)!n!]

You have a typo? should read n!/[(n-k)!k!]
 
mathman said:
You have a typo? should read n!/[(n-k)!k!]

yes

yes the part in the brackets where n is above k is nCk
also expressible as
n!/[(n-k)!k!]
 

Similar threads

Undergrad Number of possible unique outcomes help - Binomial
  • · Replies 1 ·
Replies
1
Views
3K
Use of binomial theorem in a sum of binomial coefficients?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Negative Poisson-Binomial Distribution
  • · Replies 14 ·
Replies
14
Views
6K
MHB How Do You Calculate Binomial Probabilities for Survey Representation?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Newton's Generalized Binomial Theorem
  • · Replies 3 ·
Replies
3
Views
3K
Binomial expansion of term with x^2
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad What is the Binomial Theorem and How is it Proven?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Can the Binomial Theorem be derived without prior knowledge of the formula?
  • · Replies 6 ·
Replies
6
Views
4K
Binomial theorem - not an easy question
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Question about proof of Great Picard Theorem
  • · Replies 3 ·
Replies
3
Views
3K