1.(A)(i)Show that 2+4+6+8+..+2n=n(n+1).
(ii)Find the sum of the first 200 even numbers.
(iii)Find the sum of the first 200 odd numbers.
(B)(i)Use the formula at the beginning of the question to find the sum of the first 2n natural numbers.

Marquise has 200 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width w w (in meters) is modeled by: a ( w ) = − w 2 + 1 0 0 w a(w)=−w 2 +100w what side width will produce the maximum garden area? meters