(20 points) Recall that the binomial theorem states that for any integer n20 and variables x and y, one has the expansio

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20 Points Recall That The Binomial Theorem States That For Any Integer N20 And Variables X And Y One Has The Expansio 1 (42.87 KiB) Viewed 12 times

(20 points) Recall that the binomial theorem states that for any integer n20 and variables x and y, one has the expansion ΑΝΑ where (x + y)" = Σ -Σ (1) =Σ(1) h=0 b. Show that = k!(n - k)! I and zero otherwise. With this statement, answer the following questions. a. Using special values of x and y, show that n! if 0 < k < m, Σ(*) - k=0 Σ() - r. = 2k = 2" and Σ Σ(3) k=0 |k = n2n-1 and verify by numerically verifying your result in the case n = 3. (Hint: Use differentiation.) c. Show that 72 Σ (7) k² = 2ª-²n(n+1). k=0