Use the Principle of Mathematical Induction to show that the given statement is true for...

70.2K

Verified Solution

Question

Accounting

image
image
image
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

Answer & Explanation Solved by verified expert
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students