The first picture is my problem The third picture is an exam

The first picture is my problem. The third picture is an example of the same type of problem, and on the bottom of the example by the \"(1)\" are what the choices are for the drop down arrow in my problem except with different numbers. Thank you!!

Use the Principle of Mathematical Induction to show that the following statement is true for all natural numbers n 8 +16 +24 What two conditions must the given statement satisfy to prove that it is true for all natural numbers? Select all that apply D The statement is true for the natural number 1 The statement is true for any two natural numbers k and k +1 If the statement is true for the natural number 1, it is also true for the next natural number 2 D If the statement is true for some natural numberk, it is also true for the next natural number k +1 Show that the first of these conditions is satisfied by evaluating the left and right sides of the given statement for the first natural number 8 16 +24. +8n An (n +1) 8 8 simplify your answers.) To show that the second condition is satisfied, write the given statement for k +1 8 +16 +8k 8(k +1) 4(k 1) (k +2) (Simplify your answers. Type your answers in factored form.) If the statement for k +1 is true whenever 8 16 24 +8k k (k +1) holds for some k the given statement 8 +16 +24 +8n J An (n 1) s true for all natural numbers se the statement for k 8 +16 +8k k(k +1), to simplify the left side 4 k (k +1) 8 (k 1) k +2 Use the distributive rule and the associative rule to rewrite the right side 4k (k +8(k 4 k(k 8 (k Use this result to draw a conclusion regarding the given stateme 8 +16 +24 +8n 4n(n +1) O A. Since the right side of the statement for k +1 simplifies to the left side of the statement for k, the second condition required to prove that the given statement is true for all natural O B. Since this statement cannot be shown to be true for all values of k, the second condition required to prove that the given statement is true for all natural numbers is not satisfied. H O C. Since this statement is true for all values of k, the second condition required to prove that the given statement is true for all natural numbers is satisfied. The first condition in the F

Solution

Yes

The answers which you have mentioned are correct!

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