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When using proof by induction we most often prove a statement P for positive integers n. We think about the problem in a domino-toppling fashion. The first step is to write out P(n=1), so inserting 1 for ...

As the triangle in the question is a right angled triangle we can use Pythagoras Theorem , a²+b²=c². c is the size of the longest size which is what we are looking for an...

When we're doing algebra and expanding brackets, our first step is to multiply everything inside each bracket by what we have just before the bracket. Let's start with the 4(x+5). 4 lots of our unknown my...

An even number is any number that can be divided by two to give a whole number. If we define "n" as "any whole number", we can say that "2n" is an even number. Odd numbers ca...

Start by expanding the brackets: (Take special care to remember the minus sign when expanding the second bracket as this is a common mistake)= 62x + 63 - 3x - x(1/x)Simplify further:= 12...