The electric field from an infinitely large and uniformly charged sheet is independent of the distance from the sheet, yet the individual charges in the sheet all produce fields that object the inverse square law. Why doesn't the field get weaker at greater distances?

Answer 1

Are you calculus based?
If so, you know the field contributions in the direction perpendicular to the plane increases as the angle from far charges increases (due to the angle), that increases as the field from the close particles decreases.