Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Part b assume the statement is true for n = k. prove that it must be true for n = k + 1, therefore proving it true for all natural numbers, n. t hint: since the total number of dots increases by n each time, prove that d (k) + (k + 1) = d(k+1).

Sagot :

d( k+1) is only true when d(k) is true ,  d(1) should also be true for d(k+1) statement to be true.

What is Mathematical Induction ?

For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.

It is given that

the statement is true for n = k

According to the principle of Mathematical Induction

Let d(n) be a statement involving Natural Number n such that

  • [tex]\rm d(1) \;is\; true[/tex]

  • [tex]\rm d(m) \;is\; true[/tex]

  • [tex]\rm d(m +1)\; is\; true[/tex]

So ,  the statement d(n) is true for all the n natural numbers.

According to the second principle of Mathematical Induction

Let d(n) be a statement involving Natural number n such that

  • [tex]\rm d(1) \;is\; true[/tex]

  • [tex]\rm d(m) \;is\; true[/tex] when [tex]\rm d(n) is true[/tex] for all n where 1 ≤ n ≤m .

  • Then the statement [tex]\rm d(n) is true[/tex] for all the values of n ( natural number)

Therefore , d( k+1) is only true when d(k) is true , also d(1) should also be true.

To know more about Mathematical Induction

https://brainly.com/question/1333684

#SPJ1

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.