あげる => ...Up (Upwards) N4
Direction
あげく => to end up; in the end; finally; after all ~ N2
てあげてくれ => to do for; to do a favor N3
Coercion
たあげく => After A, B was the final/end result N2
Reason, Result, Response
させてあげる => (Allow) N4
Allow
にあげます => give, take N5
Give it away
...てあげてください => to do for; to do a favor N4
Benefit
てあげる => Help, do for N4
Give and take advice
あげくのはてに (は) => finally; in the end; on top of all that N2
Result
[上「あ」]げる => Just finished/completed A N3
Time, Situation
てさしあげる => Do for N4
Give and take advice
てあげる => to do for; to do a favor N5