If 1+2x+3x210=a0+a1x+a2x2+…+a20x20, then a1 equals

The general term in the expansion of1+2x+3x210 is10!r!s!t!1r(2x)s3x2t where r+s+t=10=10!r!s!t!2s×3t×xs+2tWe have to find a1 i.e. the coefficient of x.For the coefficient of x1, we must haves+2t=1But, r+s+t=10∴ s=1−2t and  r=9+t, where  0≤r,s,t≤10.Now, t=0⇒s=1, r=9For other values of t, we get negative values of s. So, there is only one term containing x and its coefficient is10!9!1!0!×21×30=20Hence, a1=20ALITER     We have, 1+2x+3x210=10C0+10C12x+3x2+10C22x+3x22+…+10C102x+3x210∴ a1= Coeff. of x=20.