Search over 10,000 free study notes

Sum(1/n) is shown to converge by bracketing the series correctly and then comparing it with a series we know diverges. Sum(1/n^2) can be shown to converge via the integral test (using y=1/x^2), where the...

This question is based on MAT 2015 question 2. This question has already built up the generalized difference of two powers in the buildup. We can apply this to aⁿ - 1 to give: aⁿ - 1...

Right! Analysing the function "y" we can see that the graph should not exist below the "x" axis, since all the elements that form "y" as a function are positive, no matter wh...

We need to maximise the value of (a^2)b given that a+b = 20.The first step is to note that we can eliminate b from these equations to give a problem in just one variable. We have b = 20 - a, so (a^2)b = (...

Firstly lets rearrange the equation to get rid of cos^2(x) to make it easier to solve by using the identity sin^2(x)+cos^2(x) = 1. Then we get 2sin^2(x) - 4sin(x) + 1 - sin^2(x) + 2 = sin^2(x) - 4sin(x) +...