Consider the function f$($x$)=1(15$x$)2.($a$)$ Find the indicated coefficients in the following power series identity, valid on some nonempty interval centred at x$=0$:$()$f$($x$)=$n$=0$cnxn$.$c$0=$

c$1=$

c$2=$

c$3=$

c$4=($b$)$ Find the radius of convergence of the series in line $().$