# APM - Q2 - Finding a general result

## 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.