How do I prove that expansion has no constant term?

Answer 1

an expansion for f(x) does not have constant term

if x is a factor for series expansion of

f(0) = 0

for example sin x but cos x has a constant term 1

actually f(0) is the constant term

Answer 2

Usually the constant is the value at 0.
If you look at the power series for sin, you'll see that it doesn't have a constant term. Actually, you can say that it has one but the value is zero.