(This is not HW, even though it may look a bit like it.) Using the notation nCr in the combinatorics meaning, The sum of ((n+k)Cn)*((1/2)^(n+k)) from k = 0 to n equals one. Why? (I thought it might use the identity (n+1)Cr = nCr+nC(r-1), but that didn't get me anywhere.) Thanks in advance for any pointers.