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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...

The cake is in the shape of a circle. How many degrees in a circle?

Abi is 9 years old so the angle of her slice is 9 x 10 = 90°, Elvera is 14 years old so her angle is 14 x 10 = 140°. Total angle ...

The enhanced greenhouse effect is the stronger impact caused by human emissions of greenhouse gases. Greenhouse gases include carbon dioxide, methane and water vapour and are often produced by burning fos...

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...