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Unformatted text preview: m containing x3 in the expansion (2x − y )5 (b) The term containing x117 in the expansion (x + 2)118 √ 7 8 (c) The term containing x 2 in the expansion ( x − 3) (d) The term containing x−7 in the expansion 2x − x−3 (e) The constant term in the expansion x + x−1 5 8 5. Use the Prinicple of Mathematical Induction to prove n! > 2n for n ≥ 4. n 6. Prove j =0 n j = 2n for all natural numbers n. (HINT: Use the Binomial Theorem!) 7. With the help of your classmates, research Patterns and Properties of Pascal’s Triangle. 8. You’ve just won three tickets to see the new film, ‘8.9.’ Five of your friends, Albert, Beth, Chuck, Dan, and Eugene, are interested in seeing it with you. With the help of your classmates, list all the possible ways to distribute your two extra tickets among your five friends. Now suppose you’ve come down with the flu. List all the different ways you can distribute the three tickets among these five friends. How does this compare with the first list you made? What does...
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