なくて済む/ないで済む => get by without doing ~ N2
ずに済む => get by without doing ~ N2
~ます/~ません => Polite, present form N5
Verb suffixes
ずにすませる => Get something done without doing A N1
Miscellaneous
ません => be not doing something N5
Result status
させてください/させてもらえますか/させてもらえませんか => please let me do N3
て済む => sufficient by; no problem to; resolve by ~ N3
せいにする => Blame... N2
Cause, reason
ませんでした => Did not... N5
Negation in the past
姿を見せる => figure; appearance N3
Ability
させてあげる => (Allow) N4
Allow
てみせる => I'll show you ~ N4
Purpose, target