Binomial Theorem
What is the value of 1.01 to the power 10? Expanding it by hand means ten multiplications. The binomial theorem gives the whole answer at once, term by term. In this chapter you meet Pascal's triangle, write the expansion of any power of a sum, find a single term without writing the rest, and use the coefficients to answer questions on divisibility and on large numbers. Python expands powers and checks every formula.
Part of Mathematics · High School (11–12) (chapter 7)
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Pascal's Triangle and the Binomial Expansion
Pascal's triangle and the expansion of (a + b) to the power n for a whole number n. The general term, the middle term or terms, and the term that is free of x.
Properties and Applications of Binomial Coefficients
The sum of the coefficients, the relations among them, and sums that use them. Then finding remainders, proving divisibility and approximating large powers.