Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
clubcanthandlekg
Group Title
let n be a positive integer. prove that:
1(nC1) + 2(nC2) +...+n(nCn) = n2^(n1)
 one year ago
 one year ago
clubcanthandlekg Group Title
let n be a positive integer. prove that: 1(nC1) + 2(nC2) +...+n(nCn) = n2^(n1)
 one year ago
 one year ago

This Question is Open

cnknd Group TitleBest ResponseYou've already chosen the best response.0
i'll rewrite the original expression in 2 ways (and i'll call it X): X = 0(nC0) + 1(nC1) + ... + (n1)(nCn1) + n(nCn) X = n(nCn) + (n1)(nCn1) + .... + 1(nC1) + 0(nC0) now remember nCn = nC0, nC1 = nCn1, ... so if I add up the 2 equations I wrote, what do I get?
 one year ago

jishan Group TitleBest ResponseYou've already chosen the best response.0
dw:1353851927535:dw
 one year ago

jishan Group TitleBest ResponseYou've already chosen the best response.0
dw:1353852046696:dw
 one year ago

jishan Group TitleBest ResponseYou've already chosen the best response.0
dw:1353852202839:dw
 one year ago

FoolIsHere Group TitleBest ResponseYou've already chosen the best response.0
Another possible approach, will be to take the binomial expansion of \( (1+x)^n \). Differentiate both sides with respect to \( x \), then substitute \( x=1 \).
 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.