Use mathematical induction to prove the following identities. (a) [5 points] For integers n ≥ 1, 71 71 Σ(-1)* = (-1)"Σ T

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Use mathematical induction to prove the following identities. (a) [5 points] For integers n ≥ 1, 71 71 Σ(-1)* = (-1)"Σ T²₂ (¹ - 1) = II i=1 Assume that i = (+¹) for all integers n ≥ 1. (b) [5 points] For integers n ≥ 2, n+1 2n (c) [5 points] Suppose that a₁, az, as,... is a sequence defined as follows: a₁ 1,0₂ 8, a, a,-1+2a-2 for all integers i ≥ 3. Prove that a, = 3-2-1+2 (-1)" for all integers n ≥ 1. (d) [5 points] Suppose that t₁, 12, 13,... is a sequence defined as follows: t₁ = t₂ = t3 = 1₁ t₁ = t₁-1+₁2+t₁-3 for all integers i > 4. Prove that t,< 2" for all integers n ≥ 1.