Sum of binomial coefficients

In this video, we are going to prove that the sum of binomial coefficients equals to 2^n.

[bongamsomi]

i think i understood this before. thanks for the confusion :)

[Bbarm]

why is sigma (i=0, n+1) n choose i-1 the same thing as sigma (i=0, n) n choose i ?

[grantstenger]

Quick question. At 1:51, Σ_[i=0->n+1] (n choose i) includes (n choose n+1) for the final term. This isn’t properly defined right? How is this justified/remedied?

[levels]

This doesn’t really work. First you have to show directly that if the proposition holds for n that it implies it holds for n+1. Starting with n+1 is affirming the consequent.Also your indexing does not work for summing n choose i-1. You need to explain better why you can shift the index.

[hang]

I was trying to do this for an hour!! and you helped thanks

[laujimmy]

Sum of Binomial Coefficients is easiest explained using Binomial Theorem

[SimsHacks]

Sum of (n i) = sum of (n i) 1^k 1^(n-k)=By binomial theorem (1+1)^n=2^n

[Sai-hcil]

The binomial (n -1) is undefined, you justified the step at 2:17 poorly