SOLUTION: prove that C(n,r) + C(n-1,r) + C(n-2, r) +.......+ C(r,r) = C(n+1,r+1)

Question 1045685: prove that C(n,r) + C(n-1,r) + C(n-2, r) +.......+ C(r,r) = C(n+1,r+1)
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Proceed by induction: Consider the expression + ... +
For k = 1: , and the relation is true.
Suppose the relation is also true up to k = n - r, so that
+ ... + .
===> + ... +
=
= , by a direct application of Pascal's Triangle .
Hence + ... + ,
and the relation is proved.
RELATED QUESTIONS
prove that C(n , r) + C(n , r-1) = C(n+1 ,... (answered by ikleyn)

prove that:... (answered by venugopalramana)

Show that: n C r = [(n-2) C r] + 2[(n-2) C (r-1)] + [(n-2) C (r-2)] (answered by Edwin McCravy)

Show that r(nCr) = n[(n-1)C(r-1)] (answered by Edwin McCravy)

Proof that ncr=(n/n-r)(n-1 c r) Proof that n(n-1 c r) = (r+1) (n c... (answered by math_helper)

simplify (n-1)C(r-1) +... (answered by richard1234)

Show that C(n,r)= C(n-1,r-1)+C(n-1,r) NOTE: Professor said that you can start in... (answered by jim_thompson5910)

Show that n! /r!(n-r)! + n!/(r-1)! (n-r+1)! = (n+1)!... (answered by math_helper)

For positive integers n > r, show that: a) nCr = nC(n-r) b) nCr = (n-1)C(r-1) +... (answered by swincher4391)