Please kindly help me with this question. It is better to provide hints for all of these questions. However, any help shall be much appreciated.

Thank you.

Question 2. In class we saw the following formula (for n 2 1): :32,_ n(n+1) i=1 2 ' Many students asked about how the upper and lower bounds affect this formula. You will explore that in this problem. In this problem you may use the formula above (with bounds 1 and n), and you may use TL (1) Find a formula for Z 2', and explain how you know your formula is correct. '=0 7 Z (2) Compute 2i by expanding it out. i=3 n (3) Find a formula for Z i, and explain how you know your formula is correct. (Here n 2 3. Make sure your i=3 general formula gives you the same answer as your computation in part 2.) TL (4) Find a formula for Z 2', and explain how you know your formula is correct. (Here 0 S m S n. Make sure your general formula gives you the same answer as your computation in parts 2, and your formula in part 3.) (5) Write a short reflection (about 1 paragraph) about the relationship between coming up with general formulas (parts 3 and 4), and example computations (part 2). In what ways can this approach be helpful to you