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1. Compute the following a) II2(-1)' b) 2+5+8+11+...+302+305 i c) E 100 i=1 1000! d) 998!

1. Compute the following a) II2(-1)' b) 2+5+8+11+...+302+305 i c) E 100 i=1 1000! d) 998!

C++ Programming: From Problem Analysis to Program Design
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter15: Recursion
Section: Chapter Questions
Problem 8SA
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Discrete Mathematics: Please Help me with Question 1 (See attachment)

1. Compute the following а) П-1)* b) 2+5+8+11+. .+302+305 i c) E 100 Li=1 1000! d) 998! 2. for the following recursive functions, find f(1), f(2), f(3), and f(4) f(0) = 2 f(k) =k-(f(k-1))² F(1) = 1- (((0))² = 1 – 4 = -3 F(2) = 2- ((1))? = 2 - (-3) = 5 F(3) = 3 – ((2))² = 3 – 25 = -22 F(4) = 4 - ((4))² = 4 – (-22)² = 4 – 484 = -400 n' +n 3. Prove that S, is a solution of the recursive relation 2 S, = 1 S = S1 +k for k>1 k-1 4. Using pattern recognition, solve the recursive relation f(0) = 4 f(k) = 5+1.1f(k– 1) for k>0 b) Evaluate f(10) 5. Prove: n' + 5nis divisible by 6 for all integer n20. 6. Use mathematical induction to prove that 2+5+8+11+......+(3n-1)-n(3n+1)/2 7. A person borrowed $4000 on a bank credit card at a nominal rate of 24% per year, which is actually charged at a rate of 2% per month. a) what is the effective annual percentage rate (Effective APR) for the card? b) Assume that the person does not place any additional charges on the card and pays the bank $300 each month to pay off the loan. Let B(n) be the balance owed on the card after n months. Find explicit formula for B(n). c) How long will be required to pay off the debt? d) What is the total amount of money the person will have paid for the loan? 8. Solve the recursion: A = 1; A2 = -1 Ar = 5Ak-1-6Ax-2 x+1 9. Let f(x) = %3! 2x-4 a) Find domain of f(x) b) Prove that f(x) is one-to-one
Transcribed Image Text:1. Compute the following а) П-1)* b) 2+5+8+11+. .+302+305 i c) E 100 Li=1 1000! d) 998! 2. for the following recursive functions, find f(1), f(2), f(3), and f(4) f(0) = 2 f(k) =k-(f(k-1))² F(1) = 1- (((0))² = 1 – 4 = -3 F(2) = 2- ((1))? = 2 - (-3) = 5 F(3) = 3 – ((2))² = 3 – 25 = -22 F(4) = 4 - ((4))² = 4 – (-22)² = 4 – 484 = -400 n' +n 3. Prove that S, is a solution of the recursive relation 2 S, = 1 S = S1 +k for k>1 k-1 4. Using pattern recognition, solve the recursive relation f(0) = 4 f(k) = 5+1.1f(k– 1) for k>0 b) Evaluate f(10) 5. Prove: n' + 5nis divisible by 6 for all integer n20. 6. Use mathematical induction to prove that 2+5+8+11+......+(3n-1)-n(3n+1)/2 7. A person borrowed $4000 on a bank credit card at a nominal rate of 24% per year, which is actually charged at a rate of 2% per month. a) what is the effective annual percentage rate (Effective APR) for the card? b) Assume that the person does not place any additional charges on the card and pays the bank $300 each month to pay off the loan. Let B(n) be the balance owed on the card after n months. Find explicit formula for B(n). c) How long will be required to pay off the debt? d) What is the total amount of money the person will have paid for the loan? 8. Solve the recursion: A = 1; A2 = -1 Ar = 5Ak-1-6Ax-2 x+1 9. Let f(x) = %3! 2x-4 a) Find domain of f(x) b) Prove that f(x) is one-to-one
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