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anonymous
 4 years ago
let n be a positive integer. prove that:
1(nC1) + 2(nC2) +...+n(nCn) = n2^(n1)
anonymous
 4 years ago
let n be a positive integer. prove that: 1(nC1) + 2(nC2) +...+n(nCn) = n2^(n1)

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i'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?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1353851927535:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1353852046696:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1353852202839:dw

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