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Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 1+7+72+ ... +70-1 _ 1/2 (70-1) What is the first step in an induction proof? O A. Show that the statement is true for n=k. O B. Show that the statement is true for n=k+1 O C. Show that the statement is true for n=1 OD. Show that the statement is true for n=0. Complete the steps to show that the statement is true for the appropriate value of n. 1+7+72+...+77-1 = 1/2 (70-1). 70-1?16)-1) Simplify both sides What is the next step in an induction proof? A Assume that the given statement holds for some k and determine whether it then holds for k +1 OB. Determine whether the given statement holds for some k C. Determine whether the given statement holds for any number k + 1 Click to select your answer(s). Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n 1+7+72+....h -1 _ 1/2 (70-1). OC. Determine whether the given statement holds for any number k+1. OD. Assume that the given statement holds for k=1, and determine whether it holds for k=2 Write the given statement fork + 1 1+7+72 ....k-1. (Do not simplity Use integers or fractions for any numbers in the expression) Now, according to the Principle of Mathematical Induction, assume that 1+7+72.....7-1 Use this assumption to express the k. 1 terms on the left side of the statement for k=1 as a single term with a denominator of 6 (Simplify your answer) is the resulting statement for k+ 1 true? A Yes, because when written as a single term the expression on the left side is the same as on the right side of the statement for k=1 B. Yos, because evaluating the left side whenk 1 gives the same result as obtained above for evaluating the night side of the given statement when n C. Yes, because multiplying both sides of the statement by 6 and simplifying results in the same expression on both sides OD. No, because it cannot be determined whether the same statement is true for all values of 1 Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 1+7+72+...+70-1 1 / 4 (70-1) (Do not simplify Use integers or fractions for any numbers in the expression) Now, according to the Principle of Mathematical Induction, assume that 1 +7+72....+7K-12 Use this assumption to express the k+ 1 terms on the left side of the statement for k+1 as a single term with a denominator of 6. (Simplify your answer.) Is the resulting statement for k+ 1 true? ment for O A Yos, because when written as a single term, the expression on the left side is the same as on the right side of the statement for k=1 OB Yes, because evaluating the left side when k-1 gives the same result as obtained above for evaluating the right side of the given statement when n=1 OC. Yes, because multiplying both sides of the statement by 6 and simplifying results in the same expression on both sides OD. No, because it cannot be determined whether the same statement is true foral values of k Use the results obtained above to draw a conclusion about the given statement Since 1.7.72.....7-1 = (0-1) satisfies of the conditions listed in the Principle of Mathematical Induction, this statement is

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