If f(x)=(x+1)(x+2)(x+3)...............(x+400).,then, find coefficient of x^19

Short answer: 1Explanatio:Consider a polynomial of the form f(x)=(x+a)(x+b). The "x" term in every parentheses has co-efficient as 1. So the co-efficient of x^2 in (x+a)(x+b) when expanded will also be equal to 1. This we can say that any equation of the form (x+a1)(x+a2)(x+a3)...(x+an) will have co-efficient of 1 in its "x^n" term. Therefore for x+1(x+2)(x+3)....(x+400) we can ignore everything after (x+19) and so we can say that the co-efficient of x^19=1