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.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d (k+ 1).

Question

04-07-2022
Mathematics

Answered

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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.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d (k+ 1).

Sagot :

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AFOKE88 AFOKE88 · Answer 1 · 2022-07-06T12:53:14-04:00

The inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.

How to carry out Mathematical Induction?

Suppose we have the statement 3n > 4n for all positive integers n.

Now, the statement above is false when n = 1 , since 3 is less than 4. However, it will be true for all other positive integers.

In that case, we can still prove this statement by induction for all integers n ≥ 2 .

Thus, the inductive step is assuming that the statement is true for some n = k , where k is one of the values we want to prove the statement for, it shows that it is also true for n = k+1.

Read more about Mathematical Induction at; https://brainly.com/question/24672369

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How to carry out Mathematical Induction?

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