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For this explanation we will use the following example from a 2013 exam paper: If u 1 = 2 and u n+1 =(5u n -3)/(3u n -1), then prove that u n =(3n+1)/(3n-1) for all n>=1 The first step of any proof by ind...

This problem is all about using integration by parts, so let's start by quoting the formula for integration by parts: ∫u*(dv/dx)dx = uv - ∫v*(du/dx)dx To get the integral we want on the left hand side we can...

A particle with electric charge q , mass m and velocity v in a constant magnetic field B experiences a force due to the field: F = q v X B The ' X ' ( cross-product ) means that the force is always at 90° ( ...

For any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is the sum of the square of the remaining two sides.

I recently got in to medical school and I know how hard it is. Taking Bristol med school, for example, there were around 4,500 applicants but only 220-or-so places; it is intensely competitive. I did not go ...