Answers>Maths>IB>Article

How does proof by induction work?

When using proof by induction we most often prove a statement P for positive integers n. We think about the problem in a domino-toppling fashion. The first step is to write out P(n=1), so inserting 1 for n in P. Showing that the left hand side LHS equals the right hand side RHS will prove P for n=1, so P(1). In the second step we assume that P is true for some positive integer k, so P(n=k). We write k instead of n into LHS and RHS. In the third step we evaluate P(n=k+1), so we plug in k+1 to the LHS, and use step 2 to rearrange the expression. Through rearranging we show that LHS of P(n=k+1) equals the RHS expected when plugging in k+1 into P. These 3 parts connect to form a proof for all n. Since we can say k=1, and we showed P(k+1) is true if P(k) is true (and we know P(k)=P(1) is true), we can say P(2) is true. Then repeating this mechanism means that P(3), P(4), P(5), ... are all true, thereby proving P(n) for all positive integers n.

Answered by Ana C. Maths tutor

1303 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

How do you perform implicit differentiation?


If the fourth term in an arithmetic sequence is, u4 = 12.5, the tenth is u10 = 27.5. Find the common difference and the 20th term.


Three girls and four boys are seated randomly on a straight bench. What is the probability that the boys sit together and the girls sit together.


The sum of the first n terms of an arithmetic sequence is Sn=3n^2 - 2n. How can you find the formula for the nth term un in terms of n?


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