Thread: combinatoric identity

i got this bunch of questions from my math teacher and i dont think i can do them...but this seems to be the most challenging of them all.. if you can solve it plz help me...

show that the sum of the coefficients of the 'r' term and of the (r+1) term in the expansion of (1+x)^n is equal to the coeffiecient of the (r+1) term in the expansion of (1+x)^(n+1). How is this result connected with Pascal's triangle?

Gosh i dont even know how to start this problem.. any help would be greatly appreciated
thank you

Originally Posted by phatjigga

i got this bunch of questions from my math teacher and i dont think i can do them...but this seems to be the most challenging of them all.. if you can solve it plz help me...

show that the sum of the coefficients of the 'r' term and of the (r+1) term in the expansion of (1+x)^n is equal to the coeffiecient of the (r+1) term in the expansion of (1+x)^(n+1). How is this result connected with Pascal's triangle?

Gosh i dont even know how to start this problem.. any help would be greatly appreciated
thank you

It is called Pascal's Identity.
And we use it to prove the inductive step in the binomial expansion.