Скачать или смотреть IB Paper One - Proof by Mathematical Induction (Fully Worked Solution)

A maths exam questions for Higher Level maths students on the topic of mathematical induction.

Proving that 4^n+15n-1 is divisible by 9 by mathematical induction for all positive integer values of n.

This question is taken from the international baccalaureate (IB) Paper 1 of the Higher Level (HL) Mathematics Exam from May 2017 (it is question 8).

The Four Steps of Mathematical Induction
1) Show that P(1) is true
Let n=1 and work it out.
2) Assume P(k) is true
Replace all of the n’s with k's and assert that they are true.
3) Show that P(k) implies P(k+1)
Use P(k) to show that P(k+1) is true.
4) End the proof
Write, “Since P(1) is true and the truth of P(k) implies
P(k+1) is true, then by the principle of mathematical
induction, P(n) is true for all positive integers of n”

I hope it helps :)

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