22: Core Pure - Proof by Induction: Series
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Introducing Proof by Induction
Introducing Proof by Induction
A1-01 Proof by Induction: An Introduction
A1-01 Proof by Induction: An Introduction
Sums of Series
Sums of Series
A1-02 Proof by Induction: Sum of the first n Natural Numbers
A1-02 Proof by Induction: Sum of the first n Natural Numbers
A1-03 Proof by Induction: Sum of the first n Square Numbers
A1-03 Proof by Induction: Sum of the first n Square Numbers
A1-04 Proof by Induction: Sum of the first n Cube 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
A1-05 Proof by Induction: Sum(r(r+1))=n(n+1)(n+2)/3
A1-06 Proof by Induction: Sum(r.r!)=(n+1)!-1
A1-06 Proof by Induction: Sum(r.r!)=(n+1)!-1
A1-07 Proof by Induction: Sum(1/(r(r+1)))=n/(n+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)
A1-08 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)!
A1-09 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
A1-10 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)!
A1-11 Proof by Induction: Sum((r 2^r)/(r+2)!)=1-(2^(n+1))/(n+2)!