Question

(4) Use mathematical induction to prove that for every integer n ? 1, 1/2! + 2/3! + 3/4! + ? + n/(n + 1)! = 1 - 1/(n + 1)!. (5) Use mathematical induction to prove that for every integer n ? 1, 3^n + 1 ? 4^n. (6) Use mathematical induction to prove that (n - 1)n(n + 1) / 6 is an integer for all n ? 1. (Note: it's true that it is possible to prove this without induction, but in this problem you are asked to use induction—please do so!) (7) Which numbers can be obtained by adding together a collection of 4's and 9's? Decide what the answer is, and then form a statement like that in Example 7.11 in the text. Use strong induction to prove that your statement is true.

          (4) Use mathematical induction to prove that for every integer n ? 1,
1/2! + 2/3! + 3/4! + ? + n/(n + 1)! = 1 - 1/(n + 1)!.
(5) Use mathematical induction to prove that for every integer n ? 1,
3^n + 1 ? 4^n.
(6) Use mathematical induction to prove that (n - 1)n(n + 1) / 6 is an integer for all n ? 1. (Note: it's true that it is possible to prove this without induction, but in this problem you are asked to use induction—please do so!)
(7) Which numbers can be obtained by adding together a collection of 4's and 9's? Decide what the answer is, and then form a statement like that in Example 7.11 in the text. Use strong induction to prove that your statement is true.

(4) Use mathematical induction to prove that for every integer n ? 1,
1/2! + 2/3! + 3/4! + ? + n/(n + 1)! = 1 - 1/(n + 1)!.
(5) Use mathematical induction to prove that for every integer n ? 1,
3^n + 1 ? 4^n.
(6) Use mathematical induction to prove that (n - 1)n(n + 1) / 6 is an integer for all n ? 1. (Note: it's true that it is possible to prove this without induction, but in this problem you are asked to use induction—please do so!)
(7) Which numbers can be obtained by adding together a collection of 4's and 9's? Decide what the answer is, and then form a statement like that in Example 7.11 in the text. Use strong induction to prove that your statement is true.

Added by Sandy M.

Question

Please give Ace some feedback