i was reading a proof on :
given that the power series converges on (-R,R) then it is continuous on the open interval(-R,R).
i know that i have to split it up into using triangular inequality where for all ε>0
δ'>o st l f(x) - f_m(x) l < ε/3
δ'' >0 st l f_m(x) - f_m(c) l < ε/3 ( continous at c).
im wondering, does δ' and δ'' depend on ε or x?