Use mathematical induction to prove the formula for all integers n ≥ 1. +33 +43 + + 3 = n²(n + 1)² 4 1³ +23 Let S be the equation 1 We will show that S, is true for every integer n ≥ 1. Select S, from the choices below. O 1³ = 1²(1 + 1)² 4 0 1² = 1³(1+1)3 4 O 13+23 = 23 (2+1) 2 O 13+23 22(2 + 1)² 4 = Sk + The selected statement is true because both sides of the equation equal Show that for each integer k ≥ 1, if Sk is true, then Sk+1 is true. Assuming S is true, we have the following. (Simplify your answers completely.) S = 13+23+33 +43 + + Then we have the following. (Simplify your answers completely.) Sk+1 = 13+23+3³ +4³ +...+ k³ + k²(k+ 1)² + 4 (k+ 1)². ( (k+ 1)². +23+33 4 4 43 + ... + n³ = n²(n + 1)² 4 (k+ 1)². (([ 4 Hence, Sk + 1 is true, which completes the inductive step and the proof by mathematical induction.

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