The McLaurin expasion for is...

(1)

... where is an 'error term' that has different interpretations. One of the most simple expression of has been found by the french mathematician Augustin Cauchy and is in that case...

, (2)

At this point You have to do the following steps...

a) setting in (2) find the value of that maximise ...

b) stting in (2) find the value of n for which is ...

Kind regards