Home > A-Level Further Maths > Teaching Order Year 1 > 22: Core Pure - Proof by Induction: Series

A1-01 Proof by Induction: An Introduction

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)!