Flashcards
2021-10-25
$$\frac{1 + 4}{2} = \frac{1 + 2 + 3 + 4}{4}$$ What general rule is this??
That the average of two numbers is also the average of the sum between them.
$$\frac{b^2 + b - a^2 + a}{b - a + 1}$$ What is the trick to simplifying this??
Realising that it’s factorising but one bracket has three terms.
$$ \frac{(b - a + 1)(a + b)}{b -a + 1} $$
What’s a trick for coming up with a formula for the sum of $k\text{th}$ powers over the integers??
Assuming that it will be equal a $(k + 1)$ degree polynomial and coming up with 5 equations.
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date: 2021-10-25 19:07
summary: how can we work out a formula for the sum of cubes?
tags:
- '@?public'
- '@?advanced-problems-in-mathematics'
- '@?notes'
- '@?maths'
title: APM - Q2 - Finding a general result