If you use the binomial theorem with a and b equal to 1 you are left with
Which is equal to
You can prove it with induction, committee argument, etc.
forgive me for my horrible english (I'm italian and I'have registred for this forum to test my language skills and to better understand the maths).
This is my question: how can i prove with the Newton's binomial that . Obviously is easy adding 1 with 1, but the book where i've found this exercise (it's "what's the mathematics?", Courant and Robbins, it's very famous) explicitly ask to use the binomial's theorem.
Thanks for the attention and for the patience.
P.s: How can I write the binomial's Coefficients on the forum?
i'm not sure that my proof are correct and that in my proof i use the newton's binomial.
if I want prove it with induction I verify basis case with and it's banal. Then I prove that if is true it must be true also for . is true (if is true )
Than it's proved? But i didn't use the binomila's theorem