Sum of Binomial Expansion
When you expand a bracket many times, a pattern starts to emerge. You can use this pattern to quickly determine the final sum of the expansion, or to find a single coefficient of an expanded variable.

The pattern that emerges can be thought of as a series of numbers. This is because each expansion follows the same pattern, so we can predict the next expansion. This is why binomial expansion is also known as “binomial series”

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a -> ar -> ar^2 -> ... -> ar^(n-1)

Just like the arithmetic series we see in C1, C2’s geometric series describe a pattern that emerges from a string of numbers.

The difference between the two is that arithmetic series add numbers together, while geometric series multiply numbers together. Because of this, our common difference from arithmetic series is replaced with a common ratio .

All formulas in this post are given to you in the exam.

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Two’s complement is the system used by computers to represent negative numbers in their binary form. The system is actually very straightforward, so it shouldn’t take long to get the hang of it!

In Two’s complement, all negative numbers are represented by a leading “1” – that is: their first digit (starting from the left) is a 1. You then work backwards, and all digits that are represented by a “1” you subtract from the leading value.

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