Question 2. In class we saw the following formula (for n 2 1): :22 = n(n + 1)6(2n + 1) 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). (1) Find a formula for Z 2'2, and explain how you know your formula is correct. i=0 8 (2) Compute Z 712 by expanding it out and adding all the numbers together. i=4 n (3) Find a formula for 2 2'2, and explain how you know your formula is correct. (Here n 2 4. Make sure your i=4 general formula gives you the same answer as your computation in Part 2 when you subsitute n = 8.) (4) Now you will work with a general starting index m and a general end index n (additionally 0 g m g 72..) n Find a formula for Z 732, and explain how you know your formula is correct. (Make sure your general i=m formula gives you the same answer as your computation in Part 27 and your formula in Part 3.) (5) Write a short reection (about 1 paragraph) about the relationship between coming up with general formulas (Parts 3 and 4)7 and example computations (Part 2). In what ways can this approach be helpful to you in other problems