For (1 + x)m + n Tr+1 = m+nCr xr for coefficient of xm, r = m i.e coefficient is m+nCm and for coefficient of xn, r = n i.e. coefficient is m+nCn ⇒ Ratio of coefficient of xm to xn is m+nCmm+nCn=m+nCm+n-mm+nCn=m+nCnm+nCn=1
The coefficient of xm in (1+x)m+(1+x)m+1+.....+(1+x)n, m £ n is