Induction for each integer n 2 1, define the sum s(n) as follows i(i+1) 12 2 3 3-4 for example, s(1) s(2)=? and -i(i +1)-1-2 2 12 2.3 3 i. [2 points] compute each of the following values of s(n) and write your final answer as a fraction in lowest terms s(3) s(4) s(5)- ii. [1 point] do you see a general pattern for the simplified value of s(n) in general? write your guess to complete the proposition p(n) below for each integer n 2 1, let p(n) be the defined as the following proposition: iii. [4 points] prove that p(n) is true for all n 2 1 using a proof by induction. you must clearly state your induction hypothesis and indicate when it is used during the proof of your induction step. as usual, you must declare what each variable in your solution represents and make it clear whether each step of your proof is an assumption, something you are about to prove, or something that follows from a previous step or definition, etc