Pascals Triangle and Induction1.pdf
Pascals Triangle and Induction1.pdf
Pascals Triangle and Induction1.pdf
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Activity:In Pascal’s <strong>Triangle</strong>, colour all the odd numbers black, <strong>and</strong> leave the even numbers white. Doyou notice a pattern? Can you explain it?Look up the Sierpinski <strong>Triangle</strong> for more.Binomial formula exercises:Use the binomial expansion (or anything else you like) to solve these:a. Exp<strong>and</strong> .b. If you exp<strong>and</strong> what will the coefficient of be?c. If you exp<strong>and</strong> what will the coefficient of be?d. If you exp<strong>and</strong> is there a term independent of ? If so, what is it?e. What is the coefficient of in ?f. What is the coefficient of of in ?g. What is the highest power of inCan you find its coefficient?
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