Question: MAT 243 Week 10/15 Written Homework 1. (4 points) Use induction to prove E(2k - 1) =n2 -4 k =3 for all positive integers n

MAT 243 Week 10/15 Written Homework 1. (4 points) Use induction to prove E(2k - 1) =n2 -4 k =3 for all positive integers n 2 3. 2. (4 points) Use induction to show [ii!= (n+ 1)!-1 i= 1 is true for all positive integers n. 3. (4 points) Find a closed formula for 1 i ( i + 1 ) ' Prove your conjecture using mathematical induction. (Hint: use partial fraction decomposition for 7(41 to find a closed formula for the sum. Review "Telescoping sum" covered in the "Sequences" lecture.) 4. (4 points) Use induction to show 3 4' = 4" -4 for all positive integers n 2 2. 5. (4 points) Use induction to prove that n!

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