What is $$\sum^{1}_{r = 1} r$$??
$$ 1 $$
What do you get if you substitute $k = 1$ for $\frac{1}{2}k{k+1}$??
$$ 1 $$
How could you write out the sum that is being done for $$\sum^{k}_{r = 1} r$$??
$$ 1 + 2 + 3 + … + (k - 1) + k $$
How could you write out the sum that is being done for $$\sum^{k + 1}_{r = 1} r$$??
$$ 1 + 2 + 3 + … + k + (k + 1) $$
How could you rewrite $$\sum^{k + 1}_{r = 1} r$$??
$$ ( \sum^{k}_{r=1} r ) + (k + 1) $$
How could you rewrite $$( \sum^{k}_{r=1} r ) + (k + 1)$$ using the series formula??
$$ (\frac{1}{2}k(k+1)) + (k+1) $$
Factorise $$(\frac{1}{2}k(k+1)) + (k+1)$$??
$$ \frac{1}{2}(k+1)(k+2) $$
Substitute $k = k + 1$ into $$\frac{1}{2}k(k+1)$$??
$$ \frac{1}{2}(k+1)(k+2) $$
Simplify $$k^2(k+1) + (k+1)(3k+2)$$??
$$ (k+1)(k^2 + 3k + 2) $$
Backlinks
Metadata
date: 2020-12-10 15:44
tags:
- '@?further-maths'
- '@?induction'
- '@?public'
- '@?year-1'
title: Further Maths - Induction for Series