n Use induction to prove: for any integer n ≥ 0, Σ2 · 3³ = 3n+¹ − 1. j=0 Base case n = Σ2.30 j= Inductive step Assume that for any k > = we will prove that 2.3³ - Σ2.3 = Σ2.3+ j=( j= = 3. + 3n+1 1 = Σ2.3³= = By inductive hypothesis

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Q: # 2. Use mathematical induction II to prove that for all integers n 2 5, 1 + 4n < 2".

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