Assume that
![[Graphics:Images/BigOMod_gr_57.gif]](../Images/BigOMod_gr_57.gif){kind=small}
and ![[Graphics:Images/BigOMod_gr_58.gif]](../Images/BigOMod_gr_58.gif){kind=small}
, and ![[Graphics:Images/BigOMod_gr_59.gif]](../Images/BigOMod_gr_59.gif){kind=small}
. Then(i)
![[Graphics:Images/BigOMod_gr_60.gif]](../Images/BigOMod_gr_60.gif){kind=small}
, (ii)
![[Graphics:Images/BigOMod_gr_61.gif]](../Images/BigOMod_gr_61.gif){kind=small}
, (iii)
![[Graphics:Images/BigOMod_gr_62.gif]](../Images/BigOMod_gr_62.gif){kind=small}
,provided that
![[Graphics:Images/BigOMod_gr_63.gif]](../Images/BigOMod_gr_63.gif){kind=small}
. Theorem (Big "O" Remainders for Series
Approximations).
Assume that and , and . Then
(i) ,
(ii) ,
(iii) ,
provided that .
Exploration.
![[Graphics:../Images/BigOMod_gr_64.gif]](../Images/BigOMod_gr_64.gif)
![[Graphics:../Images/BigOMod_gr_65.gif]](../Images/BigOMod_gr_65.gif)
(c) John H. Mathews 2004