## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: 12.[Maximum mark: I OI(a)(b)Find the sum Of the infinite geometric sequence 27 , —9, 3Use mathematical induction to prove that for n e ,[3 marks][7 marks]

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: Yes Question Answer Transcription of this question: [Maximum mark: 18]oLet A =11011 and B:001o(a)(b)(c)Given that X and Y -B(i)(ii)find X and Y;does x-i +Yhave an inverse

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: 8. mark: 8]Prove by mathematical induction E = I , n e Z*

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: 13.imum mark: 20](a)(h)(c)Show that sin 2nx —sin ((2n + l) + _Ilence prove, hy induction, thatsin 2nxcosx + cos3x cos5x + + — l) x) —2 sin xforall neT,Solve the equation cosx+cos3x— — 0 < x < n _[2 marks][12 marks][6 marks]

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: 6.imum mark: 7]Prove by mathematical induction that 1 In is divisible by 3 for all n

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: Yes Question Answer Transcription of this question: 7.imum mark: 8]Prove, by mathematical induction, that 2 , n e N , is divisible by 5.

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 7]Use the principle of mathematical induction to prove that, where n

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 7]Consider the function f (x) = , where x eR. The nth derivative of f (x) is denoted byProve, by mathematical induction, that = (2nx + nyt)el’ , n e

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 8]Use mathematical induction to prove that n(n2+ 5) is divisible by 6 for n

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: 11.[Maximum mark: 21]Consider the function fn(x) = (cos2nx) , n e(a)(b)(c)(d)Determine whether fn is an odd or even function, justifying your answer.By using mathematical induction, prove thatsin 2″ X, x — where m e Z.2″ sin 2x2Hence or otherwise, find an expression for the derivative of […]