Use the principle of mathematical induction to show that the statement is true for all natural numbers. Sn : 13 + 2 + 3' + ... + n n' (n + 1) 2 What is the first step in the induction proof? O A. Show that the statement is true for n = 1. O B. Show that the statement is true for n = k + 1. O C. Show that the statement is true for n = k. O D. Show that the statement is true for n = 0. Evaluate both sides of the statement for S, . Sy: 13 = (1) ((1) + 1)2 4 Sy : 1 = 1 (Simplify your answers.) Is S, true? O Yes O No What is the next step in the induction proof? O A. Determine whether the statement holds for any number k + 1. O B. Assume the statement holds for some k, and determine whether it then holds for k + 1. O C. Determine whether the statement holds for some k. O D. Assume that the statement holds for k = 1, and determine whether it holds for k = 2. Carry out the next step in the proof.Use the principle of mathematical induction to show that the statement is true for all natural numbers. S: 13 + 2" + 3 3 + ...+3- 1 (n+1)2 Carry out the next step in the proof. Assume SK: 13 + 23+ 33 + ...+ 3 - k(k+1)2 4 is true for some natural number k. Prove Sk + 1: 13 + 23 + 33 + ... + K3 + (k + 1)3 = (Simplify your answer. Type your answer in factored form.) Rewrite the left side of Sk + 1- 13 + 2 + 3" + ... + * + ( * + 1 ) = ] + ( k + 1) 3 (Use integers or fractions for any numbers in the expression.) Rewrite the expression on the right in the previous step as one fraction. 1 3 + 2 " + 3 " + .. . + K + ( k + 1 ) 3 = [ (Simplify your answer. Type your answer in factored form. Use integers or fractions for any numbers in the expression.) Is Sk + 1 true? O No O Yes What is the next step in the induction proof? O A. The statement is true for S, but does not hold for Sk + 1, given that it holds for k. We have disproved S, by the principle of mathematical induction. O B. The statement is true for S and Sk+ 1, given that it holds for k. All that remains is to show that theUse the principle of mathematical induction to show that the statement is true for all natural numbers. 3_ n2{n+'l}2 _3 3 s Sn.t +2 +3 +---+n 4 (Simplify your answer. Type your answer in factored form} Rewrite the left side of Sk +1. 3 t3 +23+33 +---+k3+{k+1]3= |:|+{lt+ 1) (Use integers or fractions for any numbers in the expression.) Rewrite the expression on the right in the previous step as one fraction. 13 +23+33 +---+l