How do you prove that when you expand a binomial like $(a+b)^n$ the coefficients can be calculated by going to the n row in Pascal's triangle?

So for instance, if you wanted to expand $(a+b)^n$ using Pascal's triangle you would use the formula $\sum_{k=0}^{n} \frac{n!}{k!(n-k)!}a^{n-k}b^k$ I understand why $\sum_{k=0}^{n} \frac{n!}{k!(n-k)!}$ gives you the n row of each entry in pascals triangle but how do you prove that Pascal's triangle is related to the coefficients of a binomial expansion in the frist place.

  • Kav10 Kav10

    Low bounty!

    • Is this a complicated question? What bounty do you recommend?

    • Thanks so much for that detailed explanation it means a lot. I was really struggling with that concept since I've been self-teaching myself and didn't have anyone to ask.

  • Kav10 Kav10

    No problem! I am glad you liked it. That’s what this website is for :-) Ask your questions and get help :-)


Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer

1 Attachment

Kav10 Kav10
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.