binomial theorem

1(a) Find nCk+(n+1)Ck+(n+2)Ck+....+(n+m)Ck , where k smaller than or equal
to n
1(b) Using (a), show that
m+4
Σr(r-1)(r-2)(r-3)=24[(m+5)C5 - 1]
r=5

Hence evalute
k
Σr(r-1)(r-2)(r-3) for k greater than or equal to 4
r=0

2.show that nC0．nCr+ nC1．nC(r+1)+.....+nC(n-r)．nCn= (2n)!/(n+r)!(n-r)!

3.consider the sequence Un in which U1=0, Un+1=2n-Un for n = 1,2,......
using M.I.,show that 2Un=2n-1+(-1)^n for n=1,2,........