Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
fpmaker
Group Title
Binomial Expansion:
(n choose k) + (n choose (k+1))...need to use the factorial form to go through to step and eventually prove the answer... = ((n+1) choose (k+1))...
 one year ago
 one year ago
fpmaker Group Title
Binomial Expansion: (n choose k) + (n choose (k+1))...need to use the factorial form to go through to step and eventually prove the answer... = ((n+1) choose (k+1))...
 one year ago
 one year ago

This Question is Open

across Group TitleBest ResponseYou've already chosen the best response.1
\[\begin{align} \binom nk+\binom n{k+1}&=\frac{n!}{k!(nk)!}+\frac{n!}{(k+1)!(nk1)!}\\ &=\frac{1}{nk}\left[\frac{n!(k+1)}{(k+1)!(nk1)!}+\frac{n!(nk)}{(k+1)!(nk1)!}\right]\\ &=\frac{(n+1)!}{(k+1)!(nk)!}=\binom{n+1}{k+1}. \end{align}\]
 one year ago

fpmaker Group TitleBest ResponseYou've already chosen the best response.0
Thank you! My algebra with factorials is a little weak..is there any way you could briefly explain how you got to each step? Thanks again!!
 one year ago

across Group TitleBest ResponseYou've already chosen the best response.1
The only algebraic manipulation that's worth mentioning is that \(n!=n(n1)!\). Both the LHS and the RHS on first line are selfexplanatory. On the second line, I factored out \((nk)^{1}\) from both terms (notice I multiplied the second term by \(nk\)) to equate denominators (using the idea I just mentioned). Finally, I just expanded and added the numerators on the third line to prove the equality.
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.