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For n = 1, the sum is given by (1/2)(1)(1+1), which gives 1, the expected result. We now assume that the statement is true for some k. If we look at k+1, the sum is given by 1 + 2 + ... + k + (k+1). Since...

The function f(x) is a product of 2 functions of x, so when we differentiate it, we need to use the product rule.

The product rule states that for a function f(x) = g(x)*h(x), f'(x) is given by g(x...

Eutrophication occurs when excess nutrients, like nitrates and phosphates, enter a body of water. These excess nutrients cause an increase in plant and algal growth in the water, often leading to an algal...

The difference between the A* and lower grades in A-Level English - and the following is true for both the exam and coursework - is the ability to do two things:

1. an analysis of techniques...

Integrate this = (3x^3)/3 + (3x^2)/2 + c So y = x^3 + (3x^2)/2 + c Using point (0,0), 0 = 0 + 0 + c so c = 0. Full equation of the curve is therefore x^3 + (3x^2)/2