Please ASAP ? Use the Principle of Mathematical Induction to show that the following statement is true for all natural numbers n.9+8+7+... + (10-n) =n(19-n).....What two conditions must the given statement satisfy to prove that it is true for all natural numbers? Select all that apply.The statement is true for the natural number 1.If the statement is true for the natural number 1, it is also true for the next natural number 2.If the statement is true for some natural number k, it is also true for the next natural number k+1.The statement is true for any two natural numbers k and 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 nu9+8+7+ + (10 - n) = -n(19-n)D= (Simplify your answers.)To show that the second condition is satisfied, write the given statement for k + 1.9+8+7+ ... + (10 - k) +=(Use integers or fractions for any numbers in the expression. Type your answer in factored form.)Now, according to the Principle of Mathematical Induction, assume that 9+8+7+ ..+(10- k) =.(Simplify your answer. 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.)What can be done to show that the resulting statement for k+1 is true? (Do not simplify. Type your answer in factored form. Use integers or fractions for any numbers in the expression.)What can be done to show that the resulting statement for k+1 is true?O A. Factork out of each side of the statement to demonstrate that the resulting equation is true for all natural numbers k> 0.O B. Substitute 1 for k and evaluate each side of the statement to show that they have the same value.O C. Multiply the left and right sides of the statement by 2 and simplify each side to the same expression.D. Write the terms of the expression on the left side over a common denominator and factor the numerator to make the expression onSince both conditions of the Principle of Mathematical Induction are satisfied, the given statement 9 + 8+7+.+(10 -n)=¬n(19- n) is trueClick to select your answer(s).MacBook Proesc24%

Use the Principle of Mathematical to shown that the statement is true for all natural numbers n, we…

Use the Principle of Mathematical Induction to show that the following statement is true for all natural numbers n. 9+8+7+ +(10-n) =5n(19-n) ...... What two conditions must the given statement satisfy to prove that it is true for all natural numbers? Select all that apply. The statement is true for the natural number 1. If the statement is true for the natural number 1, it is also true for the next natural number 2. If the statement is true for some natural number k, it is also true for the next natural number k+1. The statement is true for any two natural numbers k and 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 9+8+7+… + (10-n)" 악(19-n) = (Simplify your answers.) To show that the second condition is satisfied, write the given statement for k+ 1. 9+8+7+ ... + (10-k) +=O (Use integers or fractions for any numbers in the expression. Type your answer in factored form.) Now, according to the Principle of Mathematical Induction, assume that 9+8+7+ ... + (Simplify your answer. Use integers or fractions for any numbers in the expression. ) +(10-k)=. 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.) What can be done to show that the resulting statement for k1 i O O O D

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 39E