The coefficient of xr in the expansion of (1+x)n is given by nCr. Therefore, the coefficient of x5 in the given expansion is calculated as, Coeff x5=21C5+22C5+......+30C5 =21C6+21C5+22C5+....+30C5)−21C6 =(22C6+22C5+....+30C5)−21C6 Expanding in the similar pattern further, cocffx5=(31C6+30C5)−21C6 =31C6−21C6