Hi, Everyone Every one this assignment involved multiple parts in this question.

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Hi, Everyone

Every one this assignment involved multiple parts in this question. Please help me .Thank you

Proof We prove the result by mathematical induction i Taking squareroot of both sides, we get VTi+2l Si2l. Therefore, base case holds. iii. Suppose that the result holds for some integer k with k 2 2, that is iv. Consider n = k + 1. Let A2-12 + + zf Then, vi. Then we get, VA2+rk+ rrrk V. Hence viii. So the result holds forn k1 Therefore, the result holds for all positive integers n by the principle of mathematical induction Is this proof correct? (A) Yes (B) No Is this a proof by strong induction? (A) Yes (B) No

Explanation / Answer

Is the proof correct?

(A) Yes.

The inductive hypothesis assumed the result for a single integer k. Therefore, this is simple induction.

Is this a proof by strong induction?

(B) No.

Which of the following justifies the inequality?

Since there are only two terms, this is

(A) Base case.

vi. The assumption of the inductive hypothesis is taken as RHS.

The answer is (B) Induction hypothesis.

The proof is complete.

(A) Yes, enough detail is provided.

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