Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers. 13 + 23 + 3 3 +... +3 _ n ( n + 1) 2 4 Evaluate Doin sides of the statement at the appropriate value of n. 13+ 23+ 33 +...+ 3 - 12 ( n + 1 ) 2 4 1 = 1 (Simplify your answers.) What is the second condition that the given statement must satisfy to prove that it is true for all natural numbers n? O A. The statement is true for natural number k + 1. B. The statement is true for any two natural numbers k and k + 1. O C. If the statement is true for some natural number k, it is also true for the next natural number k + 1. D. If the statement is true for the natural number 1, it is also true for the next natural number 2. Write the given statement for k + 1. 13 + 23 + 33 + ... + K3 + ] = 4 (Simplify your answer. Type your answer in factored form. Use integers or fractions for any numbers in the expression.) According to the Principle of Mathematical Induction, assume that 13 + 23 +33 + ...+k3 =]. (Simplify your answer. Type your answer in factored form. Use integers or fractions for any numbers in the expression.) Use this assumption to rewrite the left side of the statement for k + 1. What is the resulting expression? Do not simplify. Type your answer in factored form. Use integers or fractions for any numbers in the expression.)