Prove that n mod 2 = ¡ 1−(−1) n ) /2. Find and prove a similar expression for n mod 3 in the form  where ω is the complex number 2. Evaluate the sum  by substituting  and summing first on k. Does your...

Prove that n mod 2 = ¡ 1−(−1)ⁿ
) /2. Find and prove a similar expression for n mod 3 in the form
 where ω is the complex number

2. Evaluate the sum
 by substituting
 and summing first on k. Does your answer agree with (3.26)?