Question

Use the iteration technique to solve the following recurrence relations in terms of n.

Answer 1

To solve the recurrence relation using the iteration technique, follow the steps: derive the general form of the relation, express it in terms of previous terms, iterate through the terms, and verify the solution. An example is provided to illustrate the process.

Step-by-step explanation:

To solve the recurrence relation using the iteration technique, we can follow the given steps:

1. Derive the general form of the recurrence relation by analyzing the pattern in the terms.
2. Express the relation in terms of the previous terms using indices.
3. Iterate through the terms to find a pattern or formula.
4. Verify the solution by substituting values and checking if the equation holds true for all values of n.

For example, if we have the recurrence relation an = an-1 + n, we can start by expressing it in terms of the previous term: an = an-1 + n. Then, we can iterate through the terms: an = an-1 + (n-1) + n. Simplifying, we get an = an-1 + 2n - 1. This can be further simplified to an = a1 + 2n(n+1)/2 - n = a1 + n(n+1).