(Solved): Please Answer all of it! Question 3. (2 points) Consider the statement \( Q_{n}: n^{2}+5 n+3 \) is ...

Please Answer all of it!

Question 3. (2 points) Consider the statement \( Q_{n}: n^{2}+5 n+3 \) is an even integer where \( n \in N \). It can be shown that if \( Q_{n} \) is true, then \( Q_{n+1} \) is also true. What can you say about the truth value of \( Q_{n} \) for arbitrary \( n \in \) N? Briefly justify your answer. Question 4. (11 points) Provide a proof using Mathematical Induction of the following statement: For all \( n \in N, 2^{1}+2^{2}+2^{3}+\cdots+2^{n}=2^{n+1}-2 \) You are only required to provide careful details of the inductive hypothesis and inductive step.