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
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
- 1710 views
- $20.00
Related Questions
- How do you go about solving this question?
- Solving Inequalities- Erik and Nita are playing a game with numbers
- Sinusodial graph help (electrical)
- How do you do absolute value equations with inequalities?
- Algebra Question 3
- Graph the pair of equations in the same rectangular coordinate system: Y=-2x ; y=-2
- Let $f(x,y,z)=(x^2\cos (yz), \sin (x^2y)-x, e^{y \sin z})$. Compute the derivative matrix $Df$.
- Differentiate $f(x)=\int_{\sqrt{x}}^{\arcsin x} \ln\theta d \theta$
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 :-)