Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers. n(2n-1)(2+1) 1²+

Business, Finance, Economics, Accounting, Operations Management, Computer Science, Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Algebra, Precalculus, Statistics and Probabilty, Advanced Math, Physics, Chemistry, Biology, Nursing, Psychology, Certifications, Tests, Prep, and more.
Post Reply
answerhappygod
Site Admin
Posts: 899603
Joined: Mon Aug 02, 2021 8:13 am

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers. n(2n-1)(2+1) 1²+

Post by answerhappygod »

Use The Principle Of Mathematical Induction To Show That The Statement Is True For All Natural Numbers N 2n 1 2 1 1 1
Use The Principle Of Mathematical Induction To Show That The Statement Is True For All Natural Numbers N 2n 1 2 1 1 1 (53.73 KiB) Viewed 55 times
Use The Principle Of Mathematical Induction To Show That The Statement Is True For All Natural Numbers N 2n 1 2 1 1 2
Use The Principle Of Mathematical Induction To Show That The Statement Is True For All Natural Numbers N 2n 1 2 1 1 2 (53.43 KiB) Viewed 55 times
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers. n(2n-1)(2+1) 1²+3²+5²+(2n-15²- The first condition that the given statement must satisfy in proving that it is true for all natural numbers n is that this statement is true for n Evaluate both sides of the statement at the appropriate value of n 1²+3² +5² ++ (2n-1)²n(2n − 1)(2n +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? OA. If the statement is true for the natural number 1, it is also true for the next natural number 2 OB. The statement is true for any two natural numbers k and k+ 1. OC. If the statement is true for some natural number k it is also true for the next natural number k + 1 OD. The statement is true for natural number k+1 Write the given statement for k+1. P²+3²+5²0-12² (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 1 3²+5+(2k-1²-0 (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 simplity Type your answer in factored form Use integers or fractions for any numbers in the expression) Is the resulting statement for +1 true? COOO OA. Yes, because writing the terms of the sum on the left side over the least common denominator and dividing out common factors results in the same expression as on the right side OB. Yes because writing the terms of the sum on the left side over a common denominator of 3 and simplifying results in the same expression as on the right side OC. No, because it cannot be determined whether the same statement is true for all values of k An Von har stinking but the statement and s

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers. n(2n-1)(2+1) 1²+3² +5² +(2n- n-1²- -(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? OA. If the statement is true for the natural number 1. it is also true for the next natural number 2 OB. The statement is true for any two natural numbers k and k+1. OC. If the statement is true for some natural number K, it is also true for the next natural numberk+1 OD. The statement is true for natural number k+1 Write the given statement for k + 12 2.3.50-1².04 (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 1+3+5+(2k-1)² ] (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 fork 1 What is the resulting expression? (Do not simplity Type your answer in factored form. Use integers or fractions for any numbers in the expression) Is the resulting statement fork 1 true? atrs) OA. Yes, because writing the terms of the sum on the left side over the least common denominator and dividing out common factors results in the same expression as on the right side OB. Yes, because writing the terms of the sum on the left side over a common denominator of 3 and simplifying results in the same expression as on the right side OC. No, because it cannot be determined whether the same statement is true for all values of k OD. Yes, because multiplying both sides of the statement by 3 and simplifying results in the same expression as on the right side Use the results obtained above to draw a conclusion about the given statement (n-1) (2n-1)(2+1) satisfies of the conditions listed in the Principle of Mathematical Induction, this statement is
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!
Top
Post Reply

Return to “Archived Questions & Answers”