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Chapter 1 Summary - Coggle Diagram
Chapter 1 Summary
Binomial Theorem
Pascal's Triangle 
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Infinite series (1 + x)^a = (1 + ax) + (a(a - 1) / 2!)x^2 + (a(a - 1)(a - 2) / 3!)x^3 + ... + (a(a + 1)(a - 2)...(a - r + 1) / r!)x^r + ...
Factorials
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When order is not important, this is a combination
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Sequences
Geometric
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General Pattern: Un = U1(r)^n - 1, (r != 1, 0, -1) (U1 != 0)
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Proofs
Proof by Contradiction
1. Identify what is being implied
2. Assume the implication is false 3. use axioms, theorems, etc to arrive at a contradiction
4. state that this proofs the implied statement is true
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Series
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Geometric
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When |r| < 1, the numbers get so small that you are basically adding nothing: converges
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