Use mathematical induction to prove the formula for all integers n ≥ 1.1³ + 2³ +3³ +4³ + ... + ³ _ n²(n + 1)²4Let S be the equation 13 + 23 +33 +43 +...+n³חWe will show that S is true for every integer n ≥ 1.Select S₁ from the choices below.1O 1³ = 1²(1 + 1)²40 1² = 1³ (1 + 1)³4O 1³ + 23 = 2³(2 + 1)2O 13 +23 22(2 + 1)²4The selected statement is true because both sides of the equation equalkk+1Show that for each integer k ≥ 1, if S is true, then SAssuming S is true, we have the following. (Simplify your answers completely.)S₁ = 13+23+33 +4³ + ... += Sk+Then we have the following. (Simplify your answers completely.)Sk+1 = 1³ +23+33 +4³ + + k³ +Hk²(k+ 1)²4(k + 1)² .(k+ 1)².(k+ 1)²+n²(n + 1)²n³ =44441²is true.Hence, Sk + 1 is true, which completes the inductive step and the proof by mathematical induction.

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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.