So just want to make sure getting this right.
Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon’s damage. The extra damage is 2d8 for a 1st-level spell slot, plus 1d8 for each spell level higher than 1st, to a maximum of 5d8. The damage increases by 1d8 if the target is an undead or a fiend, to a maximum of 6d8.
Improved Divine Smite
By 11th level, you are so suffused with righteous might that all your melee weapon strikes carry divine power with them. Whenever you hit a creature with a melee weapon, the creature takes an extra 1d8 radiant damage.
Ok so say have an 11th level Pal. They attack with a longsword which is 1D8, according to Improved Divine Smite all of his attacks get an extra 1D8 radiant automatically, then cause use their spell slots to add even more radiant damage?