Answers>Maths>IB>Article

How should I approach a proof by induction question?

Proof by induction is a powerful proof technique that can be used to prove a certain property and is a common question on the IB exams. Consider for instance the problem "Prove that sinx + sin3x +...+ sin((2n-1)x) = sin^2 n x/sinx". The essential components of an inductive proof are as follows:Consider the case when n = 1Assume true for n = k, for some kProve true by demonstrating that the pattern holds for n = k+1Conclude the proof.Step 2 just requires you to replace any instance of "n" in the problem with a "k". Proof by induction problems are often worth 6-7 marks on the exam, and doing steps 1 and 2 correctly is a surefire way of picking up 2-3 marks for free. A useful tip to consider after doing step 2 is that you should write the "goal"you are trying to achieve on the side. In other words, write out the k+1 case so you know what you're looking for as you work through the steps. The lovely thing about proof by induction is that you can easily do it by working through it formulaically. All you need is for your algebra skills to be solid!

Answered by Aditya R. Maths tutor

1143 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

The sum of the first and third term of a geometric sequence is 72. The sum to infinity of this sequence is 360, find the possible values of the common ratio, r.


Solve the equation sec^2 x+ 2tan x = 0, 0 ≤ x ≤ 2π. IB May 2017 Exam


When the polynomial 3x^3 +ax+ b is divided by x−2 , the remainder is 2, and when divided by x +1 , it is 5. Find the value of a and the value of b.


The sixth term of an arithmetic sequence is 8 and the sum of the first 15 terms is 60. Find the common difference and list the first three terms.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences