Problem 2. Partial Sums & Induction Consider the sequence with the i-th term being i.(1+1); so the first three terms are (a) Compute the partial sums of the first n terms of this sequence when: 1 1 1 2'6'1 (i) (ii) n= 1, n= 2, n= 3. (b) Based on your above answer, make a conjecture about the partial sum of the first n terms in this sequence for general n E N, n 1. Your conjecture should be of the form i=1 (+1) (c) Prove your above conjecture using induction. Be sure to clearly show/state your base case, inductive hypothesis, what you wish to prove using the IH, and inductive step (see practice problem for guidance if you're unclear what is expected).