A1: Proof by Induction

Home > A-Level Further Maths > Pure > A: Proof > A1: Proof by Induction

From the DfE Mathematics AS and A-Level Further Maths Content (LINK):

PLAYLIST

Introducing Proof by Induction

A1-01 Proof by Induction: An Introduction

Sums of Series

A1-02 Proof by Induction: Sum of the first n Natural Numbers

A1-03 Proof by Induction: Sum of the first n Square Numbers

A1-04 Proof by Induction: Sum of the first n Cube Numbers

A1-05 Proof by Induction: Sum(r(r+1))=n(n+1)(n+2)/3

A1-06 Proof by Induction: Sum(r.r!)=(n+1)!-1

A1-07 Proof by Induction: Sum(1/(r(r+1)))=n/(n+1)

A1-08 Proof by Induction: Sum((2r-1)^2)=(1/3)n(4n^2-1)

A1-09 Proof by Induction: Sum(r/(r+1)!)=((n+1)!-1)/(n+1)!

A1-10 Proof by Induction: Sum(2r+1)/(r^2(r+1)^2)=1-1/(n+1)^2

A1-11 Proof by Induction: Sum((r 2^r)/(r+2)!)=1-(2^(n+1))/(n+2)!

Divisibility

A1-12 Proof by Induction: Divisibility Test Introduction

A1-13 Proof by Induction: 9^n-1 is divisible by 8

A1-14 Proof by Induction: 6^n+4 is divisible by 5

A1-15 Proof by Induction: 3^(2n)+11 is divisible by 4

A1-16 Proof by Induction: 2^n+6^n is divisible by 8

Sequences

A1-17 Proof by Induction: Sequence u_(n+1) = 1 - 2u_n

A1-18 Proof by Induction: Sequence u_(n+1) = 4u_n - 6

A1-19 Proof by Induction: Sequence u_(n+1) = 3u_n - 2^n

A1-20 Proof by Induction: Sequence u_(n+1) = u_n + n(3n + 1)

A1-21 Proof by Induction: Sequence u_(n+1) = (u_n)/(1 + u_n)

Matrices

A1-22 Proof by Induction: Matrices Example 1

A1-23 Proof by Induction: Matrices Example 2

A1-24 Proof by Induction: Matrices Example 3

A1-25 Proof by Induction: Matrices Example 4

Inequalities

A1-26 Proof by Induction: Inequality Example 1

A1-27 Proof by Induction: Inequality Example 2

A1-28 Proof by Induction: Inequality Example 3

A1-29 Proof by Induction: Inequality Example 4

A1-30 Proof by Induction: Inequality Example 5

A1-31 Proof by Induction: Inequality Example 6

Extras

A1-32 Proof by Induction: Proving de Moivre's Theorem

A1-33 Proof by Induction: Product Rule and Equivalent Forms Problem

A1-34 Proof by Induction: nth Derivative of x^2 e^x