Discrete Mathematics: Please Help me with Question 7 (See attachment) ### Mathematical Problems and Exercises1. **Compute the following:** - a) $\prod_{n=2}^{58} (-1)^n$ - b) $2 + 5 + 8 + 11 + \ldots + 302 + 305$ - c) $\sum_{i=0}^{100} \frac{i}{1000!}$ - d) $\frac{1000!}{998!}$2. **Evaluate the Recursive Functions:** - For the given recursive relation, find $f(1)$, $f(2)$, $f(3)$, and $f(4)$: \[ f(0) = 2 \] \[ f(k) = k - (f(k-1))^2 \] - Solutions: - $f(1) = 1 - (f(0))^2 = 1 - 4 = -3$ - $f(2) = 2 - (f(1))^2 = 2 - (-3)^2 = 5$ - $f(3) = 3 - (f(2))^2 = 3 - 25 = -22$ - $f(4) = 4 - (f(3))^2 = 4 - (-22)^2 = -400$3. **Proof of Recursive Solution:** - Prove that $S_n = \frac{n^2 + n}{2}$ is a solution of the recursive relation: \[ S_1 = 1 \] \[ S_k = S_{k-1} + k \quad \text{for } k > 1 \]4. **Pattern Recognition:** - Use pattern recognition to solve the recursive relation: \[ f(0) = 4 \] \[ f(k) = 5 + 1.1f(k-1) \quad \text{for } k > 0 \] - Evaluate $f(10)$5. **Proof of Divisibility:** - Prove: $n^3 + 5n$ is divisible by 6 for all integer \(n \ge

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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?

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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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