factorials-20 points The factorial function is written: n! and is the product of all integers from 1 to n. Give a formula for i (!) and prove your answer correct. (Hint: make some tables of relevant quantities for small values of i. For example, i! has values 1, 2, 6, 24, 120, 720... i * i! has values 1,4, 18, 96, 600, 5020.... The sum will have values 1,5, 23.... Use this to guess the right formula. Then use induction to prove it.) 1. Give the entries in your tables, up to n = 7 (1 point) 2. Write the conjectured function for the sum. Your function can use exponents, factorials, cases, or any other common mathematical symbols. (5 points) 3. Write precisely the equation you are proving by induction. Make sure that it is an equation, not just the definition of a function.(2 points) 4. Prove the base case of the induction. (2 points) 5. What is the induction assumption? (2 points) 6. What is the goal in the induction step? (2 points) 7. Prove the induction step. (5 points) 8. Conclude that the equation is true for all n > 1. (1 point)