4. Prove the following statements using an inductive argument: _n(n+1)(2n+1) 6 72 a. Σiª: = i=1 12 b. If a = 2a- and b =

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4. Prove the following statements using an inductive argument: _n(n+1)(2n+1) 6 72 a. Σiª: = i=1 12 b. If a = 2a- and b = 1-(1-a)², show that a = b for all natural numbers n. Assume that a is a fixed constant. c. Let a be the sequence defined by a₁ =1, a₁ = 8, and a₁ = a₁-11 +2a2 for n ≥ 3. Use an inductive argument to prove that if b₁ =3×2"-¹ +2(−1)", the a = b for all PL 72 neN