a) Verify that it is true for n=1. a = 2<________. b) Assuming that it is true for n-k , you get that a̟ <3. Replace 4. with a 3

in the formula for . to get an inequality, and then replace a 3 with a 6 to get a further inequality, and simplify, to show that it is true for n-k +1. a_{k+1}=\sqrt{3+a_{k}}<\sqrt{3+3}<\sqrt{3+6} a_{i+1}<\sqrt{3+6} a_{i+1}< \text { 3. For the sequence }\left\{a_{x}\right\} \text { with } a_{1}=2 \text { and } a_{\text {ont }}-\sqrt{3+a_{n}} ; n \geq 1 use Mathematical Induction to prove that a. <3 for all natural numbers, n.