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.
Math Gnome
87
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
2K
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
- 1975 views
- $20.00
Related Questions
- Prove that $1+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{n}} \leq 2 \sqrt{n}-1$
- Let $f(x,y,z)=(x^2\cos (yz), \sin (x^2y)-x, e^{y \sin z})$. Compute the derivative matrix $Df$.
- Recursive square root sequence
- Find $x$, if $\sqrt{x} + 2y^2 = 15$ and $\sqrt{4x} − 4y^2 = 6$.
- Algebra Word Problem #1
- Solving Inequalities- Erik and Nita are playing a game with numbers
- True or false
- Center of algebra of functions
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.
No problem! I am glad you liked it. That’s what this website is for :-) Ask your questions and get help :-)