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 $\sum_{k=0}^{n} \frac{n!}{k!(nk)!}a^{nk}b^k$ I understand why $\sum_{k=0}^{n} \frac{n!}{k!(nk)!}$ 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.
Math Gnome
85
Answer
Answers can only be viewed under the following conditions:
 The questioner was satisfied with and accepted the answer, or
 The answer was evaluated as being 100% correct by the judge.
1 Attachment
Kav10
1.9K
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.
 answered
 1611 views
 $20.00
Related Questions
 Value Of Investment
 How do you go about solving this question?
 Let $z = f(x − y)$. Show that $\frac{\partial z}{\partial x}+\frac{\partial z}{\partial y}=0$
 Find an expression for the total area of the figure expressed by x.

The given equation is x²  2mx + 2m  1=0
Determine m.  Solving for two unknown angles, from two equations.
 How to adjust for an additional variable.
 Reverse this equation/function (2d to isometric)
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 selfteaching myself and didn't have anyone to ask.
No problem! I am glad you liked it. That’s what this website is for :) Ask your questions and get help :)