4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and...
3. Let P(n) be the statement that a postage of n cents can be formed using just 3-cent stamps and 5-cent stamps. The 5 / Induction and Recursion parts of this exercise outline a strong induction proof that P(n) is true for n 18. a) Show statements P(18), P(19), P(20), and P(21) are true, completing the basis step of the proof. b) What is the inductive hypothesis of the proof? c) What do you need to prove in the inductive...
Prove the statement n cents of postage can be formed using just 4-cent and 11-cent stamps using mathematical induction, where n ≥ 30. Click and drag the given steps (on the right) to the corresponding step names given on the left) to carry out the inductive steps of the proof, after the inductive hypothesis has already been assumed in (b). Step 1 Replace eight 4-cent stamps by three 11-cent stamps, and we have formed k+ 1 cents in postage (3....
Use strong induction to show that any amount of postage more than one cent can be formed using just two-cent and three-cent stamps. (please be detailed!)
Please show all the steps and explain. Prove that every amount of postage of 18 cents or more can be formed using just 4-cent and 7-cent stamps Prove that every amount of postage of 18 cents or more can be formed using just 4-cent and 7-cent stamps
Problem 1 148pts] (1) I 10pts! Let P(n) be the statement that l + 2 + + n n(n + 1) / 2 , for every positive integer n. Answer the following (as part of a proof by (weak) mathematical induction): 1. [2pts] Define the statement P(1) 2. [2pts] Show that P(1 is True, completing the basis step. 3. [4pts] Show that if P(k) is True then P(k+1 is also True for k1, completing the induction step. [2pts] Explain why...
Instructions: Please show all of your work. Unsupported answers may receive no credit. 1. (20 pts) Use mathematical induction to show that for integers n 21, 2.21 +3.22 + ... + (n + 1)21 = n. 21+1 w 2. (20 pts) Let P(n) be statement that a postage of n cents can be formed using only 4-cent and 7-cent stamps. Using strong induction, prove P(n) is true for n 2 18.
need steps A small post office has only 4-cent, 6-cent and 10-cent stamps Find a recurrence relation for the number of ways to form postage of n cents if the order of the stamps matters, i.e.. different orderings add to the count a. b. How many ways are there to form postage of 20 cents? Fill in the following chart 10 14 6 8 16 20 0 40 18 Extra Credit: A small post office has only 4-cent, 6-cent and...
Use mathematical induction to prove that the statement is true for every positive integer n. 1'3+ 24 +3'5 +...+() = (n (n+1)(2n+7))/6 a. Define the last term denoted by t) in left hand side equation. (5 pts) b. Define and prove basis step. 3 pts c. Define inductive hypothesis (2 pts) d. Show inductive proof for pik 1) (10 pts)
Let S(n) be a statement parameterized by a positive integer n. Consider a proof that uses strong induction to prove that for all n 4.S(n) is true. The base case proves that S(4), S(5), S(6), S(7), and S(8) are all true. Select the correct expressions to complete the statement of what is assumed and proven in the inductive step. Supposed that for k> (1?),s() is true for everyj in the range 4 through k. Then we will show that (22)...
please show by using the following version of induction: 2.3.28 Prove the formula for the sum of a geometric series: Can - 1) an-1 +an-2 + ... +1 a-1 • BASIS STEP: Show that P(n) is true for n = no. • INDUCTIVE STEP: Assume that P(n) is true for some n no. (This is called inductive hypothesis). Then show that the inductive hypothesis implies that P(n + 1) is also true.