Covers: the terms sequence, series, deductive definition, inductive definition, arithmetic sequence, and geometric sequence notation to express the terms in a sequence about sigma notation. (Integral for HE)
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Introduction and constructing arithmetic sequences, introduction and constructing geometric sequences, modelling with sequences, and general sequences. (Khan Academy)
Covers: First term, common difference, nth term, arithmetic series, sum of arithmetic series, and problem-solving with sequences and series. (integral for HE)
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Covers: First term, common ratio, nth term, geometric series, sum of geometric series, infinite geometric series, convergent geometric series (common ratio between -1 and 1), and sum to infinity of a convergent geometric series. (Integral for HE)
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The sum of the first n natural numbers The sum of the squares of the first n natural numbers, the sum of the cubes of the first n natural numbers and the method of differences. (Integral for HE)
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Constructing and presenting a proof using mathematical induction for the sum of a series, the nth term of a sequence or the nth power of a matrix. (Integral for HE)
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Using the method of differences with partial fractions to sum a series, using proof by induction to prove divisibility results. (Integral for HE)
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