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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
(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?
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