6. By sight from the curves graphed to the solution to problem #5, it appears that the circumscribed area converges to Pi faster than the inscribed area. Below we also plot the differences to see which ones go to zero first.

Input := 

InError = Pi - n/2 Sin[2 Pi/n];
CircError = Pi - n Tan[Pi/n];

Input := 

Plot[InError, {n, 10, 400},
 AxesLabel -> {"n", "Inscribed Error"},
 DisplayFunction -> $DisplayFunction]

Output =

-Graphics-

Input := 

Plot[CircError, {n, 10, 400},
 AxesLabel -> {"n", "Circumscribed Error"},
 DisplayFunction -> $DisplayFunction]

Output =

-Graphics-