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This is the first part of a Step 1 question (2012 question 8), and is fairly typical in that it requires A Level Maths understanding to be applied in a number of different ways, out of the usual context.W...

The ELAT is an unsual test for one main reason: it has no questions. Instead you are faced with six poems or extracts from texts, which all have a shared theme. Themes in the past have included Journey...

Introduction

Start simple, with a sentance stating which way you will be arguing, and a second sentance summarising your argument. For example, "I will be arguing that..."...

We know that x_n > x_(n+1) is true if and only if x_n - x_(n+1) > 0 is true.So x_n - x_(n+1) = (n^3 − 9n^2 + 631) − ((n + 1)^3 − 9(n + 1)^2 + 631) = (n^3 − n^3 − 3n^2 − 3n − 1) − 9(n^2 − n^2 − 2n − ...

If we want to prove it, we need to prove every odd number can be expressed as the difference of two squares, which is very easy.

Suppose this odd number to be 2n-1, then we can see 2n-1=n...